This site is supported by donations to The OEIS Foundation.


From OeisWiki
Jump to: navigation, search

"Steven R. Finch's incredible labor of love, an encyclopedia of mathematical constants, begins with such basics, then moves on to more elaborate topics. ... It appears astonishing to me that a single individual went through all these topics. His achievement can only be compared to the On-Line Encyclopedia of Integer Sequences." [Osmo Pekonen, 2019]

"As a researcher in combinatorics, one of my favorite tools is the On-Line Encyclopedia of Integer Sequences, or OEIS. This database was started by the mathematician Neil Sloane, who first started keeping an index of popular sequences of integers that came up in his work. At the time, Sloane was a graduate student at Cornell University. A photo of the first page of Sloane’s notebook is shown in Figure 7.1. Recognize any of these sequences?" [T. Kyle Petersen, 2019]

"... we'd like to thank to OEIS editors Michel Marcus, Peter Luschny, Jon E. Schoenfield and others for their patient, faithful volunteer work and for useful comments and suggestions during the editing of sequences, concerned with this manuscript." [Kolosov Petro. 2019]

"On p. 18, notes that the OEIS was used to find relevant literature." [Robert A. Proctor and Matthew J. Willis, 2017]

"All three authors would like to acknowledge the On-Line Encyclopedia of Integer Sequences [Slo14], without which this project would have been very difficult." [Nicholas Proudfoot, Max Wakefield, and Ben Young, 2015]

About this page

  • This is part of the series of OEIS Wiki pages that list works citing the OEIS.
  • Additions to these pages are welcomed.
  • But if you add anything to these pages, please be very careful — remember that this is a scientific database. Spell authors' names, titles of papers, journal names, volume and page numbers, etc., carefully, and preserve the alphabetical ordering.
  • If you are unclear about what to do, contact one of the Editors-in-Chief before proceeding.
  • Works are arranged in alphabetical order by author's last name.
  • Works with the same set of authors are arranged by date, starting with the oldest.
  • This section lists works in which the first author's name begins with P.
  • The full list of sections is: A Ba Bi Ca Ci D E F G H I J K L M N O P Q R Sa Sl T U V W X Y Z.
  • For further information, see the main page for Works Citing OEIS.


  1. Arun Padakandla, P. R. Kumar, Wojciech Szpankowski, On the Discrete Geometry of Differential Privacy via Ehrhart Theory, (2017). PDF (A103881)
  2. Arun Padakandla, P.R. Kumar, Wojciech Szpankowski, Preserving Privacy and Fidelity via Ehrhart Theory, July 2017.
  3. R. Padmanabhan, Alok Shukla, Orchards in elliptic curves over finite fields, arXiv:2003.07172 [math.NT], 2020. (A003035)
  4. Martin Paech, Numerische und algebraisch-graphentheoretische Algorithmen für korrelierte Quantensysteme, Dissertation, Hannover: Fakultät für Mathematik und Physik der Leibniz Universität, 2015.
  5. M. Paech, W. Apel, E. Kalinowski and E. Jeckelmann, Comparison of computer-algebra strong-coupling perturbation theory and dynamical mean-field theory for the Mott-Hubbard insulator in high dimensions, Phys. Rev. B 90 (24), 245147 (2014), 10 pages, doi:10.1103/PhysRevB.90.245147. Also arXiv:1410.6630, 2014.
  6. M. Paech, E. Kalinowski, W. Apel, G. Gruber, R. Loogen, and E. Jeckelmann, Ground-state energy and beyond: High-accuracy results for the Hubbard model on the Bethe lattice in the strong-coupling limit, DPG Spring Meeting, Berlin, TT 45.91 (2012).
  7. M. Paech, E. Kalinowski, W. Apel, and E. Jeckelmann, Strong-coupling expansion in the Hubbard model by a diagrammatic-combinatorial computer algorithm, DPG Spring Meeting, Dresden, TT 11.14 (2011).
  8. P. Pagacz, M. Wojtylak, On the spectral properties of a class of H-selfadjoint random matrices and the underlying combinatorics, arXiv preprint arXiv:1310.2122, 2013.
  9. Iván E. Paganini, Ruslan L. Davidchack, Brian B. Laird, and Ignacio Urrutia, Properties of the hard-sphere fluid at a planar wall using virial series and molecular-dynamics simulation, The Journal of Chemical Physics 149 (2018), 014704. doi:10.1063/1.5025332
  10. Don N. Page, Religious and Scientific Faith in Simplicity (2008); arXiv:0811.0630
  11. David Pagni, Building buildings with triangular numbers, AMATYC Review (vol. 27 no. 2 spring 2006, pp. 56-65).
  12. C. B. Pah and M. Saburov, Single Polygon Counting on Cayley Tree of Order 4: Generalized Catalan Numbers, Middle-East Journal of Scientific Research 13 (Mathematical Applications in Engineering): 01-05, 2013, ISSN 1990-9233; doi:10.5829/idosi.mejsr.2013.13.mae.9991.
  13. C. H. Pah, doi:10.1007/s10955-010-9989-5, Single polygon counting on Cayley Tree of order 3, J. Stat. Phys. 140 (2010) 198-207
  14. C. H. Pah, M. R. Wahiddin, Combinatorial Interpretation of Raney Numbers and Tree Enumerations, Open Journal of Discrete Mathematics, 2015, 5, 1-9; doi:10.4236/ojdm.2015.51001
  15. Kung-Jui Pai, Jou-Ming Chang, Ro-Yu Wu, A Constant Amortized Time Algorithm for Generating Left-Child Sequences in Lexicographic Order, International Workshop on Frontiers in Algorithmics, In: Xiao M., Rosamond F. (eds) Frontiers in Algorithmics, FAW 2017, Lecture Notes in Computer Science, vol 10336. doi:10.1007/978-3-319-59605-1_20, also in Discrete Applied Mathematics (2018). doi:10.1016/j.dam.2018.09.035
  16. I. Pak, Partition Identities and Geometric Bijections, Proc. Amer. Math. Soc. 132 (2004), 3457-3462.
  17. Igor Pak, History of Catalan numbers, arXiv:1408.5711, 2014.
  18. Igor Pak, Complexity problems in enumerative combinatorics, arXiv:1803.06636 [math.CO], 2018. (A000055, A000081, A000110, A000123, A000607, A000929, A001156, A002829, A003107, A005130, A006318, A007279, A007294, A033552, A064986, A076478, A082640, A151353, A250102)
  19. I. Pak and G. Panova, Unimodality via Kronecker products, arXiv preprint arXiv:1304.5044, 2013.
  20. Igor Pak, Greta Panova, Bounds on Kronecker coefficients via contingency tables, Linear Algebra and its Applications (2020), Vol. 602, 157-178. doi:10.1016/j.laa.2020.05.005, also PDF (A000700, A059867)
  21. I. Pak, G. Panova, E. Vallejo, Kronecker products, characters, partitions, and the tensor square conjectures, arXiv:1304.0738, 2013
  22. Igor Pak, Greta Panova, Damir Yeliussizov, On the largest Kronecker and Littlewood-Richardson coefficients, arXiv:1804.04693 [math.CO], 2018. (A003040, A070933, A110143)
  23. I. Pak, A. Soffer, On Higman's k(U_n(F_q)) conjecture, arXiv preprint arXiv:1507.00411, 2015
  24. Apisit Pakapongpun, Thomas Ward, Functorial orbit counting (2009) arXiv:0901.2646 and JIS 12 (2009) 09.2.4
  25. F. Pakovich, A. K. Zvonkin, Minimum degree of the difference of two polynomials over Q, and weighted plane trees, Selecta Mathematica, New Ser. 2014; doi:10.1007/s00029-014-0151-0
  26. M. B. Paksoy, Derived Ramanujan Primes: R'_{N}, arXiv preprint arXiv:1210.6991, 2012
  27. S. Palasek, Non-Cooperativity in Bayesian Social Learning, arXiv preprint arXiv:1407.0519, 2014
  28. Sushma Palimar and B. R. Shankar, Mersenne Primes in Real Quadratic Fields, Journal of Integer Sequences, Vol. 15 (2012), #12.5.6.
  29. J. M. Pallo, On the listing and random generation of hybrid binary trees, International Journal of Computer Mathematics, 50, 1994, 135-145.
  30. Jean Pallo, doi:10.1016/S0020-0190(00)00008-9 An efficient upper bound of the rotation distance of binary trees, Information Processing Letters, Volume 73, Issues 3-4, 29 February 2000, Pages 87-92.
  31. Jean Marcel Pallo, Weak associativity and restricted rotation, Information Processing Letters, Volume 109, Issue 10, 30 April 2009, Pages 514-517.
  32. M. Palmacci, Escher's Problem and Numerical Sequences, (2006)
  33. M. G. Palomo, Latin polytopes, arXiv preprint arXiv:1402.0772, 2014
  34. Hao Pan, Z.-W. Sun, Consecutive primes and Legendre symbols, arXiv preprint arXiv:1406.5951, 2014
  35. J. Pan, Multiple Binomial Transforms and Families of Integer Sequences, J. Int. Seq. 13 (2010), 10.4.2.
  36. Pan, Jiaqiang Some properties of the multiple binomial transform and the Hankel transform of shifted sequences. J. Integer Seq. 14 (2011), no. 3, Article 11.3.4, 8 pp.
  37. J. Pan, Matrix Decomposition of the Unified Generalized Stirling Numbers and Inversion of the Generalized Factorial Matrices, Journal of Integer Sequences, 15 (2012) #12.6.6.
  38. J. Pan, Convolution Properties of the Generalized Stirling Numbers and the Jacobi-Stirling Numbers of the First Kind, Journal of Integer Sequences, 16 (2013), #13.9.2.
  39. Qiong Qiong Pan, Jiang Zeng, The γ-coefficients of Branden's (p,q)-Eulerian polynomials and André permutations, arXiv:1910.01747 [math.CO], 2019. (A000111, A122852)
  40. Ran Pan, Block patterns in permutations and words and generalized clusters, Ph. D. Dissertation, Univ. Calif. San Diego, 2016.
  41. Ran Pan, Dun Qiu, Jeffrey Remmel, Counting Consecutive Pattern Matches in S_n(132) and S_n(123), arXiv:1809.01384 [math.CO], 2018. Also in Advances in Applied Mathematics (2019) Vol. 105, 130-167. doi:10.1016/j.aam.2019.01.005 (A001006)
  42. R. Pan, J. B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 (2016)
  43. Pan, Shu-Wen. & Pan, JQ., Direct solutions of linear non-homogeneous difference equations, Adv Differ Equ (2016) 2016: 108. doi:10.1186/s13662-016-0839-x
  44. D. Panario, M. Sahin, Q. Wang, A family of Fibonacci-like conditional sequences, INTEGERS, Vol. 13, 2013, #A78.
  45. D. Panario, M. Sahin, Q. Wang, W. Webb, General conditional recurrences, Applied Mathematics and Computation, Volume 243, 15 September 2014, Pages 220-231.
  46. A Panayotopoulos, On Meandric Colliers, Mathematics in Computer Science, (2018).
  47. A. Panayotopoulos and P. Tsikouras, "Meanders and Motzkin Words", J. Integer Sequences, Volume 7, 2004, Article 04.1.2.
  48. A. Panayotopoulos and P. Vlamos, Cutting Degree of Meanders, Artificial Intelligence Applications and Innovations, IFIP Advances in Information and Communication Technology, Volume 382, 2012, pp 480-489;doi:10.1007/978-3-642-33412-2_49.
  49. A. Panayotopoulos, P. Vlamos, Partitioning the Meandering Curves, Mathematics in Computer Science (2015) p 1-10, doi:10.1007/s11786-015-0234-0. (A000136, A005316, A000682, A000560, A217310, A217318, A227167)
  50. Kanupriya Pande, Jeffrey J. Donatelli, et al., Free-electron laser data for multiple-particle fluctuation scattering analysis, Scientific Data volume 5, Article number: 180201 (2018). doi:10.1038/sdata.2018.201
  51. Ram Krishna Pandey, "On Some Magnified Fibonacci Numbers Modulo a Lucas Number" , Journal of Integer Sequences, Vol. 16 (2013), #13.1.7.
  52. V. Pandichelvi, P. Sivakamasundari, M. A. Gopalan, On the Negative Pell Equation y^2 = 54 x^2 - 5, International Journal of Mathematics Trends and Technology- Volume 21 Number 1, pages 16-20.
  53. Sabrina X. M. Pang and Lun Lv, A Refinement of Leaves on Noncrossing Trees, Graphs and Combinatorics, 2011, doi:10.1007/s00373-011-1097-z.
  54. Alois Panholzer, Parking function varieties for combinatorial tree models, arXiv:2007.14676 [math.CO], 2020. (A000139, A006318, A010050, A214377, A294084)
  55. Alexei Pantchichkine, Constructions of p-adic L-functions and admissible measures for Hermitian modular forms, Number Theory [math.NT], 2018. Abstract (A047817)
  56. Jay Pantone, The Enumeration of Permutations Avoiding 3124 and 4312, arXiv preprint arXiv:1309.0832, 2013
  57. D. Panyushev, On the orbits of a Borel subgroup in abelian ideals, arXiv preprint arXiv:1407.6857, 2014
  58. G. Paoletti, Deterministic Abelian Sandpile Models and Patterns, Ph. D. Thesis, Universita di Pisa, Scuola di dottorato Scienze di base "Galileo Galilei", Pisa, 2013; PDF.
  59. L. A. Papakonstantinidis, The win-win-win papakonstantinidis model: The limit of the Sensitization Process (2019). doi:10.13140/RG.2.2.16575.15529 (A002162, A002391, A002392, A007524, A016627, A016628, A016629, A016630, A016631, A016632, A020862)
  60. Dimitris Papamichail, Angela Huang, Edward Kennedy, Jan-Lucas Ott, Andrew Miller, Georgios Papamichail, Live phylogeny with polytomies: Finding the most compact parsimonious trees, Computational Biology and Chemistry, Volume 69, August 2017, p. 171-177. doi:10.1016/j.compbiolchem.2017.03.013, arXiv preprint arXiv:1603.03315 [cs.DS], 2016.
  61. G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
  62. Daniel Pareja, Prime Number Races, PDF
  63. D. Parisse, The Tower of Hanoi and the Stern-Brocot Array, Thesis, Ludwig-Maximilians-Universitaet Munich, August 1997.
  64. Boram Park and Seonjeong Park, Shellable posets arising from even subgraphs of a graph, arXiv:1705.06423 [math.CO], 2017.
  65. Donghwi Park, Space-state complexity of Korean chess and Chinese chess, arXiv preprint arXiv:1507.06401, 2015.
  66. Gunwoong Park, High-Dimensional Poisson DAG Model Learning Using l_1-Regularized Regression, arXiv:1810.02501 [stat.ML], 2018.
  67. Ki-Hyeon Park and Hong-Yeop Song, Some Properties of Binary Matrices and Quasi-Orthogonal Signals Based on Hadamard Equivalence, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Vol.E95-A No.11 pp.1862-1872, 2012.
  68. Poo-Sung Park, Multiplicative functions with f(p + qn0) = f(p) + f(q) − f(n0), arXiv:2002.09908 [math.NT], 2020. (A057778, A126717)
  69. Sang-Hoon Park, Abdelmejid Bayad, Daeyeoul Kim, Divisor functions and Polygon Shape Numbers, Draft of Proceedings Book of the 2nd Mediterranean International Conference of Pure & Applied Mathematics and Related Areas (MICOPAM 2019), 1-3. PDF
  70. Seonjeong Park, Real toric manifolds and shellable posets arising from graphs, 2018. PDF (A071721)
  71. So Ryoung Park, Jinsoo Bae, Hyun Gu Kang, Iickho Song, doi:10.1090/S0025-5718-07-02082-0 On the polynomial representation for the number of partitions with fixed lengths, Math. Comp. vol. 77, no. 262 (2008) 1135-1151.
  72. Y. Park, S. Park, Avoiding permutations and the Narayana numbers, J. Korean Math. Soc. 50 (2013), No. 3, pp. 529-541, doi:10.4134/JKMS.2013.50.3.529
  73. Park, Youngja, and SeungKyung Park. "Enumeration of generalized lattice paths by string types, peaks, and ascents." Discrete Mathematics 339.11 (2016): 2652-2659.
  74. Daniel E. Parker, Romain Vasseur, Joel E. Moore, Entanglement Entropy in Excited States of the Quantum Lifshitz Model, arXiv:1702.07433 [cond-mat.stat-mech], 2017.
  75. Douglas Stott Parker and Prasad Ram, The construction of Huffman codes is a submodular ("convex") optimization problem over a lattice of binary trees. SIAM J. Comput. 28 (1999), no. 5, 1875-1905 (electronic).
  76. M. G. Parker, Conjectures on the Size of Constellations Constructed from Direct Sums of PSK Kernels, LNCS 1719, Presented in part at 13th International Symposium, AAECC-13, Honolulu, Hawaii, pp 420-429, 14-19 Nov, 1999. (postscript, PDF)
  77. M. G. Parker, Spectrally Bounded Sequences, Codes and States: Graph Constructions and Entanglement, Invited Talk at Eighth IMA International Conference on Cryptography and Coding, Cirencester, UK, 17-19 December, 2001, LNCS 2260, pp. 339ff. (2001). (PostScript, Pdf)
  78. M. G. Parker and C. Tellambura, A Construction for Binary Sequence Sets with Low Peak-to-Average Power Ratio, Reports in Informatics, University of Bergen, Report No 242, ISSN 0333-3590, February 2003. (PostScript, PDF)
  79. J. Parkkonen, F. Paulin, doi:10.2140/gt.2010.14.277, Prescribing the behaviour of geodesics in negative curvature, Geom. Topol. 14 (2010) 277-392.
  80. Bernhard R. Parodi, A generalized Fibonacci spiral, arXiv:2004.08902 [math.HO], 2020.
  81. A. Parreau, M. Rigo, E. Rowland, E. Vandomme, A new approach to the 2-regularity of the l-abelian complexity of 2-automatic sequences, arXiv preprint arXiv:1405.3532, 2014
  82. Robert Parviainen, "Lattice Path Enumeration of Permutations with k Occurrences of the Pattern 2-13", J. Integer Sequences, Volume 9, 2006, Article 06.3.2.
  83. Robert Parviainen, "Parametric Production Matrices and Weighted Succession Rules: a Dyck Path Example", J. Integer Sequences, Volume 10, 2007, Article 07.6.1.
  84. Robert Parviainen, Some bijections on set partitions (2007), arXiv:0710.1132.
  85. J. Pasukonis, S. Ramgoolam, From counting to construction for BPS states in N=4SYM, J. High En. Phys. 2011 (2) (2011) # 078 arXiv:1010.1683 doi:10.1007/JHEP02(2011)078
  86. Ludovic Patey, Ramsey-like theorems and moduli of computation, arXiv:1901.04388 [math.LO], 2019. (A000108)
  87. A. Pathak, Non-Hermitian quantum gates are more common than Hermitian quantum gates, arXiv preprint arXiv:1309.4037, 2013.
  88. Anuj Pathania, Scalable Task Schedulers for Many-Core Architectures, Ph.D. Thesis, Karlsruher Instituts für Technologie (Germany, 2018). doi:10.5445/IR/1000082991 (A000105)
  89. Anuj Pathania, Vanchinathan Venkataramani, Muhammad Shafique, Tulika Mitra, Jörg Henkel, Defragmentation of Tasks in Many-Core Architecture, ACM Transactions on Architecture and Code Optimization (TACO), Volume 14 Issue 1, April 2017, Article No. 2. doi:10.1145/3050437
  90. G. K. Patil, Ramanujan's Life And His Contributions In The Field Of Mathematics, International Journal of Scientific Research and Engineering Studies (IJSRES), Volume 1 Issue 6, December 2014, ISSN: 2349-8862;
  91. N. Patson, Pisano period and permutations of n X n matrices, Australian Math. Soc. Gazette, 2007.
  92. Elena Patyukova, Taylor Rottreau, Robert Evans, Paul D. Topham, Martin J. Greenall, Hydrogen bonding in acrylamide and its role in the scattering behavior of acrylamide-based block copolymers. arXiv:1805.09878 [cond-mat.soft], 2018. Also in Macromolecules (2018) Vol. 51, No. 18, 7032-7043. doi:10.1021/acs.macromol.8b01118 (A000108, A000309)
  93. Elena Patyukova, Taylor Rottreau, Robert Evans, Paul D. Topham, Martin J. Greenall, Supporting information: Hydrogen bonding aggregation in acrylamide: theory and experiment, Aston University (Birmingham, England 2019), S12. PDF (A000309)
  94. Paukner, M., Pepin, L., Riehl, M., and Wieser, J., Pattern Avoidance in Task-Precedence Posets, arXiv:1511.00080
  95. Neeraj Kumar Paul and Helen K. Saikia, A generalization of Fibonacci sequence, Proyecciones (2020) Vol. 39, 1393-1405. doi:10.22199/issn.0717-6279-2020-06-0085 (A000045)
  96. Shubhankar Paul, Ten Problems of Number Theory, International Journal of Engineering and Technical Research (IJETR), ISSN: 2321-0869, Volume-1, Issue-9, November 2013
  97. Shubhankar Paul, Legendre, Grimm, Balanced Prime, Prime triplet, Polignac's conjecture, a problem and 17 tips with proof to solve problems on number theory, International Journal of Engineering and Technical Research (IJETR), ISSN: 2321-0869, Volume-1, Issue-10, December 2013;
  98. G. Paun and A. Salomaa, Self-reading sequences. Amer. Math. Monthly 103 (1996), no. 2, 166-168.
  99. Chrystalla Pavlou, Edith Elkind, Manipulating citation indices in a social context, in: Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2016), J. Thangarajah, K. Tuyls, C. Jonker, S. Marsella (eds.), May 9–13, 2016, Singapore;
  100. Pavlyukh, Y.; Hübner, W. Analytic solution of Hedin's equations in zero dimensions. J. Math. Phys. 48 (2007), no. 5, 9 pp.
  101. J. Pawlewicz, Counting Square-Free Numbers, Arxiv preprint arXiv:1107.4890, 2011
  102. J. L. Pe, Ana's Golden Fractal.
  103. J. L. Pe, On a Generalization of Perfect Numbers, To appear in The Journal of Recreational Mathematics 31(3).
  104. J. L. Pe, Fractal dimension, primes and the persistence of memory, Adv. Compl. Systems 6(2) (2003) 241-249
  105. Joseph L. Pe, The 3x+1 fractal, Computers & Graphics, Volume 28, Issue 3, June 2004, Pages 431-435.
  106. Paul A. Pearce and Alessandra Vittorini-Orgeas, Yang-Baxter Solution of Dimers as a Free-Fermion Six-Vertex Model. arXiv:, 2017.
  107. Antony Pearson, On Hidden Structures in Contaminated Symbolic Data, Ph. D. thesis, University of Colorado at Boulder (2020) 27835343. PDF (A088389)
  108. Paul Peart and Wen-Jin Woan, "Generating Functions via Hankel and Stieltjes Matrices", J. Integer Sequences, Volume 3, 2000, Article 00.2.1.
  109. Paul Peart and Wen-Jin Woan, "Dyck Paths With No Peaks At Height k", J. Integer Sequences, Volume 4, 2001, Article 01.1.3.
  110. Satya R. T. Peddada, Daniel R. Herber, Herschel C. Pangborn, Andrew G. Alleyne, James T. Allison, Optimal Flow Control and Single Split Architecture Exploration for Fluid-Based Thermal Management, J. Mech. Des. (2019) 141(8), Paper No. MD-18-1843, 083401. doi:10.1115/1.4043203 Also in Proceedings of the ASME 2018 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC 2018), Quebec City, Quebec, Canada. PDF (A000041, A000262)
  111. A. Peder, M. Tombak, Finding the description of structure by counting method: a case study, SOFSEM 2011, LNCS 6543 (2011) 455-466 doi:10.1007/978-3-642-18381-2_38
  112. J. Peebles, Cap Set Bounds and Matrix Multiplication, Senior Thesis, Harvey Mudd College, 2013;
  113. E. T. Pegg Jr., A Complete List of Fair Dice, Master's Thesis, University of Colorado at Colorado Springs, 1997.
  114. Ed Pegg, Jr., Polyform puzzles, in Tribute to a Mathemagicain, Peters, 2005, pp. 119-125.
  115. Jun Pei, Li Guo, Averaging algebras, Schröder numbers, rooted trees and operads, Journal of Algebraic Combinatorics, Volume 42, Issue 1, August 2015, pp 73-109; arXiv:1401.7386.
  116. R. E. Peile, H. Taylor, Sets of points with pairwise distinct slopes, Computers & Mathematics with Applications, Volume 39, Issue 11, June 2000, Pages 109-115.
  117. Tiago P. Peixoto, Bayesian stochastic blockmodeling, arXiv:1705.10225 [stat.ML], 2017.
  118. A. Pekec, Meaningful and Meaningless Solutions for Cooperative N-person Games, European Journal of Operational Research, Volume 133, Issue 3, 16 September 2001, Pages 608-623.
  119. Osmo Pekonen, Mathematical Constants, Mathematical Constants II, The Mathematical Intelligencer (2019), 1-2. doi:10.1007/s00283-019-09929-0 Steven R. Finch's incredible labor of love, an encyclopedia of mathematical constants, begins with such basics, then moves on to more elaborate topics. ... It appears astonishing to me that a single individual went through all these topics. His achievement can only be compared to the On-Line Encyclopedia of Integer Sequences.
  120. John A. Pelesko, "Generalizing the Conway-Hofstadter $10,000 Sequence", J. Integer Sequences, Volume 7, 2004, Article 04.3.5.
  121. Jarkko Peltomäki, Privileged Words and Sturmian Words, Turku Centre for Computer Science, TUCS Dissertations No 214, August 2016;
  122. Jarkko Peltomäki and Aleksi Saarela, Standard words and solutions of the word equation X12Xn2 = (X1Xn)2, Journal of Combinatorial Theory, Series A (2021) Vol. 178, 105340. doi:10.1016/j.jcta.2020.105340 See also " arXiv:2004.14657 [cs.FL], 2020. (A000374, A002326, A037226, A330878)
  123. Jarkko Peltomäki, Markus A. Whiteland, Avoiding abelian powers cyclically, arXiv:2006.06307 [cs.FL], 2020. (A334831)
  124. J.-G. Penaud and O. Roquesm, Génération efficace d'un langage de Fibonacci, Colloque LaCIM 2000.
  125. J. Peng, Y. Zhang, Heron triangles with figurate number sides, Acta Mathematica Hungarica (2019) 1-11. doi:10.1007/s10474-018-00907-0 (A232461)
  126. Y. Peng and K. P. S. Bhaskara Rao, On Zumkeller numbers, Journal of Number Theory, Volume 133, Issue 4, April 2013, Pages 1135-1155.
  127. Yisu Peng, Y Jiang, P Radivojac, Enumerating consistent subgraphs of directed acyclic graphs: an insight into biomedical ontologies, arXiv preprint arXiv:1712.09679, 2017
  128. K. A. Penson, arXiv:quant-ph/0111151 Coherent States from Combinatorial Sequences, Conference 'Quantum Theory and Symmetries 2', Krakow, Poland, July 2001.
  129. K. A. Penson, P. Blasiak, G. Dattoli et al., Monomiality principle, Sheffer-type polynomials and the normal ordering problem (2005), arXiv:quant-ph/0510079.
  130. K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, arXiv:quant-ph/0312202 Hierarchical Dobinski-type relations via substitution and the moment problem, [J. Phys. A 37 (2004), 3475-3487]
  131. K. A. Penson, P. Blasiak, A. Horzela, G. H. E. Duchamp and A. I. Solomon, arXiv:0904.0369 Laguerre-type derivatives: Dobinski relations and combinatorial identities, J. Math. Phys. vol. 50, 083512 (2009)
  132. K. A. Penson and J.-M. Sixdeniers, "Integral Representations of Catalan and Related Numbers", J. Integer Sequences, Volume 4, 2001, Article 01.2.5.
  133. Karol A. Penson, Allan I Solomon, Coherent States from Combinatorial Sequences (2001), arXiv:quant-ph/0111151.
  134. Karol A. Penson and Karol Zyczkowski, doi:10.1103/PhysRevE.83.061118 Product of Ginibre matrices : Fuss-Catalan and Raney distribution, Phys. Rev E. 83, 061118 (2011) (9 pages). arXiv:1103.3453 arXiv version
  135. Ian Percival, Franco Vivaldi, Critical dynamics and trees, Physica D: Nonlinear Phenomena, Volume 33, Issues 1-3, October-November 1988, Pages 304-313.
  136. Carlos Castro Perelman, Generalized Fibonacci Numbers and 4k+ 1-fold symmetric Quasicrystals, Clark Atlanta University (2019). doi:10.13140/RG.2.2.13892.48001
  137. R. A. Perez, A brief but historic article of Siegel, Notices AMS, 58 (2011), 558-566.
  138. S. Perez, R. Styer, Persistence: A Digit Problem, 2013 PDF
  139. Carlos I. Pérez-Sánchez, The full Ward-Takahashi Identity for colored tensor models, arXiv preprint arXiv:1608.08134, 2016
  140. E. Pergola, Two bijections for the area of Dyck paths, Discrete Math., 241 (2001), 435-447.
  141. E. Pergola, G. Labelle, P. Leroux and R. Pinzani, Bell permutations and Stirling numbers interpolation, Proceedings FPSAC'99, Barcelona, 450-461.
  142. E. Pergola and R. Pinzani, A Combinatorial Interpretation of the Area of Schröder Paths, Electronic Journal of Combinatorics, Volume 6(1), 1999, article #R40.
  143. Elisa Pergola and Robert A. Sulanke, Schröder Triangles, Paths and Parallelogram Polyominoes, J. Integer Sequences, Volume 1, 1998, Article 98.1.7.
  144. Quinn Perian, Bella Xu, Alexander Lu Zhang, Counting the Nontrivial Equivalence Classes of Sn under {1234,3412}-Pattern-Replacement, arXiv:2008.02380 [math.CO], 2020. (A330395)
  145. Serge Perrine, About the diophantine equation z² = 32y² − 16, SCIREA Journal of Mathematics (2019) Vol. 4, Issue 5, 126-139. PDF (A000129, A001333, A002203, A046176, A082405)
  146. Jon Perry, Calculating the Smarandache numbers, in Smarandache Notions Journal (2004), Vol. 14.1, pp 124-127. PDF. (A002034)
  147. Peters, J.; Buehlmann, P. Identifiability of Gaussian structural equation models with equal error variances. Biometrika 101 (2014), no. 1, 219-228.
  148. J. Peters, J. Mooij, D. Janzing, B. Schölkopf, Causal Discovery with Continuous Additive Noise Models, arXiv preprint arXiv:1309.6779, 2013
  149. Petersen, Karl, An adic dynamical system related to the Delannoy numbers. Ergodic Theory Dynam. Systems 32 (2012), no. 2, 809-823.
  150. Karl Petersen, Ibrahim Salama, Tree shift complexity, arXiv:1712.02251 [math.DS], 2017. (A076725, A144229)
  151. Karl Petersen, Ibrahim Salama, Tree shift topological entropy, Theoretical Computer Science (2018) Vol. 743, 64-71. doi:10.1016/j.tcs.2018.05.034
  152. Petersen, K.; Varchenko, A. Path count asymptotics and Stirling numbers. Proc. Amer. Math. Soc. 140 (2012), no. 6, 1909-1919.
  153. Petersen, T. Kyle, The sorting index. Adv. in Appl. Math. 47 (2011), no. 3, 615-630.
  154. Petersen, T. Kyle On the shard intersection order of a Coxeter group. SIAM J. Discrete Math. 27 (2013), no. 4, 1880-1912.
  155. T. Kyle Petersen, Exponential generating functions and Bell numbers, Inquiry-Based Enumerative Combinatorics (2019) Chapter 7, Undergraduate Texts in Mathematics, Springer, Cham, 98-99. doi:10.1007/978-3-030-18308-0_7 (A000435) As a researcher in combinatorics, one of my favorite tools is the On-Line Encyclopedia of Integer Sequences, or OEIS. This database was started by the mathematician Neil Sloane, who first started keeping an index of popular sequences of integers that came up in his work. At the time, Sloane was a graduate student at Cornell University. A photo of the first page of Sloane’s notebook is shown in Figure 7.1. Recognize any of these sequences?
  156. T. K. Petersen, M. Guay-Paquet, The generating function for total displacement, - arXiv preprint arXiv:1404.4674, 2014
  157. T. Kyle Petersen, Bridget Eileen Tenner, The depth of a permutation, Arxiv preprint arXiv:1202.4765, 2012
  158. T. KYLE PETERSEN AND BRIDGET EILEEN TENNER, How to write a permutation as a product of involutions (and why you might care), Arxiv preprint arXiv:1202.5319, 2012 and Integers 13 (2013) A63 HTML
  159. Ivars Peterson, Fibonacci's Missing Flowers.
  160. M. D. Petkovic, doi:10.1080/10652469.2010.497998 The Hankel transform of generalized central trinomial coefficients and related sequences, Intr. Trans. Spec. Func. 22 (1) (2011) 29-44
  161. Petkovic, Marko D.; Barry, Paul; Rajkovic, Predrag Closed-form expression for Hankel determinants of the Narayana polynomials. Czechoslovak Math. J. 62(137) (2012), no. 1, 39-57.
  162. M. Petkovsek and T. Pisanski, Counting Trees, 1994. (PostScript , dvi version)
  163. M. Petkovsek and T. Pisanski, Counting disconnected structures: chemical trees, fullerenes, I-graphs and others, Croatica Chem. Acta, 78 (2005), 563-567.
  164. Petkovic, Marko D.; Rajkovic, Predrag M.; Barry, Paul The Hankel transform of generalized central trinomial coefficients and related sequences. Integral Transforms Spec. Funct. 22 (2011), no. 1, 29-44.
  165. Marko Petkovsek and Helena Zakrajsek, Enumeration of I-graphs: Burnside does it again, ARS MATHEMATICA CONTEMPORANEA, 2 (2009) 241-262. PDF
  166. Aleksandar Petojevic, "The Function _v M_m(s;a;z) and Some Well-Known Sequences", J. Integer Sequences, Volume 5, 2002, Article 02.1.7
  167. Aleksandar Petojevic, On the vMm(s*,a,z) function, Novi Sad J. Math. 34 (1) (2004) 99-106
  168. Petojevic, Aleksandar, The {K_i(z)}^\infty_{i=1} functions. Rocky Mountain J. Math. 36 (2006), no. 5, 1637-1650.
  169. A. Petojevic and N. Dapic, The vAm(a,b,c;z) function, Preprint 2013, PDF
  170. Aleksandar Petojevic, H.M. Srivastava, Computation of Euler type sums of the products of Bernoulli numbers, Applied Mathematics Letters, Volume 22, Issue 5, May 2009, Pages 796-801.
  171. A. Petras, L. Ling, S.J. Ruuth, An RBF-FD closest point method for solving PDEs on surfaces, 2018. PDF
  172. M. Pétréolle, Characterization of Cyclically Fully commutative elements in finite and affine Coxeter Groups, arXiv preprint arXiv:1403.1130, 2014.
  173. Mathias Pétréolle, Alan D. Sokal, Lattice paths and branched continued fractions. II. Multivariate Lah polynomials and Lah symmetric functions, arXiv:1907.02645 [math.CO], 2019. (A000369, A001497, A004747, A008277, A008297, A035342, A035469, A048993, A049029, A066667, A105278)
  174. George Petrides and Johannes Mykkeltveit, On the Classification of Periodic Binary Sequences into Nonlinear Complexity Classes, in Sequences and Their Applications SETA 2006, Lecture Notes in Computer Science, Volume 4086/2006, Springer-Verlag.
  175. Constantin M. Petridi, The Sums of the $ k-$ powers of the Euler set and their connection with Artin's conjecture for primitive roots, arXiv preprint arXiv:1612.07632, 2016
  176. Kolosov Petro, Relation between Pascal’s triangle and hypercubes, 2018. PDF (A007318)
  177. Kolosov Petro. An Odd-Power Identity Involving Discrete Convolution. Preprints (2019) 2019040126. doi:10.20944/preprints201904.0126.v1 ... we'd like to thank to OEIS editors Michel Marcus, Peter Luschny, Jon E. Schoenfield and others for their patient, faithful volunteer work and for useful comments and suggestions during the editing of sequences, concerned with this manuscript.
  178. Ian Petrow, MP Young, A generalized cubic moment and the Petersson formula for newforms, arXiv preprint arXiv:1608.06854, 2016
  179. V. H. Pettersson, Enumerating Hamiltonian Cycles, The Electronic Journal of Combinatorics, 21 (4) 2014, #P4.7.
  180. Ville Pettersson, Graph Algorithms for Constructing and Enumerating Cycles and Related Structures, Preprint 2015,
  181. Robertas Petuchovas, Asymptotic analysis of the cyclic structure of permutations, arXiv preprint arXiv:1611.02934, 2016
  182. A. A. Petukhov, Mixed optimization combinatorial method for constructing covering arrays, Programming and Computer Software, 2014, Vol. 40, No. 1, pp. 10-20. Pleiades Publishing, Ltd., 2014. Original Russian Text published in Programmirovanie, 2014, Vol. 40, No. 1.
  183. J. L. Pfaltz, Partitions of 2^n, Congressus Numerantium 109:3-12, 1995.
  184. J. L. Pfaltz, Partition Coefficients of Acyclic Graphs, 21st International Workshop on Graph Theoretic Concepts in Computer Science, Aachen, June 1995 (Springer Verlag, LNCS #1017) 313-332.
  185. C. Pfeifer, Probability Distribution of the Median Taken on Partial Sums of a Simple Random Walk, Stochastic Analysis and Applications, Volume 31, Issue 1, 2013, pp. 31-46; doi:10.1080/07362994.2013.741359.
  186. Götz Pfeiffer, "Counting Transitive Relations", J. Integer Sequences, Volume 7, 2004, Article 04.3.2.
  187. Goetz Pfeiffer, A Quiver Presentation for Solomon's Descent Algebra (2007), arXiv:0709.3914; Advances in Mathematics, Volume 220, Issue 5, 20 March 2009, Pages 1428-1465.
  188. Hugo Pfoertner, Uniform Illumination of a Sphere
  189. Hai Pham-Van, Linh Tran-Phan-Thuy, Cuong Tran-Manh, Bich Do-Danh, Hoang Luc-Huy, Two-Dimensional Clusters of Colloidal Particles Induced by Emulsion Droplet Evaporation, Nanomaterials (2020) Vol. 10, 156. doi:10.3390/nano10010156 (A070765)
  190. C. Phatak, R. Pokharel, M. Beleggia and M. De Graef, On the magnetostatics of chains of magnetic nanoparticles, Journal of Magnetism and Magnetic Materials, Volume 323, Issue 22, November 2011, Pages 2912-2922; doi:10.1016/j.jmmm.2011.06.058
  191. Leroux Philippe, An equivalence of categories motivated by weighted directed graphs (2007), arXiv:0709.3453.
  192. Andreas N. Philippou, Spiros D. Dafnis, A simple proof of an identity generalizing Fibonacci-Lucas identities, Fibonacci Quarterly (2018) Vol. 56, No. 4, 334-336. Abstract (A001644)
  193. Mitch Phillipson, Manda Riehl and Tristan Williams, Enumeration of Wilf classes in Sn ~ Cr for two patterns of length 3, PU. M. A. Vol. 21 (2010), No. 2, pp. 321-338;
  194. D. Phulara and L. W. Shapiro, Descendants in ordered trees with a marked vertex, Congressus Numerantium, 205 (2011), 121-128.
  195. Phakhinkon Phunphayap, Prapanpong Pongsriiam, Reciprocal sum of palindromes, arXiv:1803.00161 [math.CA], 2018. (A002113, A002385, A002779)
  196. Phakhinkon Phunphayap, Prapanpong Pongsriiam, Explicit Formulas for the p-adic Valuations of Fibonomial Coefficients, Journal of Integer Sequences, Vol. 21 (2018), Article 18.3.1. HTML (A000045, A003267, A010048, A055870)
  197. Phakhinkon Phunphayap, Prapanpong Pongsriiam, Estimates for the Reciprocal Sum of b-adic Palindromes, (2019). doi:10.13140/RG.2.2.23202.79047 (A244162)
  198. Steven T. Piantadosi, Problems in the philosophy of mathematics: A view from cognitive science, preprint.
  199. Steven T. Piantadosi, Mathematics, Substance and Surmise: Views on the Meaning and Ontology of Mathematics, University of Rochester (2019). HTML In 2009, Nathaniel Johnston found that 11630 was the smallest uninteresting number, with interestingness determined by membership in the Online Encyclopedia of Integer Sequences (OEIS)
  200. Picantin, Matthieu, Finite transducers for divisibility monoids. Theoret. Comput. Sci. 362 (2006), no. 1-3, 207-221.
  201. K Piejko, Extremal trees with respect to number of of (A, B, 2C)-edge colourings, Journal of Applied Mathematics, Hindawi Publishing Corporation, Volume 2015, Article ID 463650, 5 pages doi:10.1155/2015/463650
  202. Karin Pielage, Proactive lateral transshipments and stock allocation via transient behavior of loss systems, Master Thesis (2018) Eindhoven University of Technology (Netherlands). PDF
  203. V. U. Pierce, Continuum limits of Toda lattices for map enumeration, in Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, edited by Anton Dzhamay, Ken'ichi Maruno, Virgil U. Pierce; Contemporary Mathematices, Vol. 593, 2013.
  204. Titus Piezas III, On Ramanujan's Other Pi Formulas,
  205. Titus Piezas III, Pi Formulas, Ramanujan, and the Baby Monster Group,
  206. Titus Piezas III, Ramanujan's Constant exp(Pi sqrt(163)) And Its Cousins,
  207. Titus Piezas III, "The 163 dimensions"
  209. Giovanni Pighizzini, Limited Automata: Properties, Complexity and Variants, International Conference on Descriptional Complexity of Formal Systems (DCFS 2019) Descriptional Complexity of Formal Systems, Lecture Notes in Computer Science (LNCS, Vol. 11612) Springer, Cham, 57-73. doi:10.1007/978-3-030-23247-4_4 (A007814)
  210. Giovanni Pighizzini and Luca Prigioniero, Limited Automata and Unary Languages, In: Charlier É., Leroy J., Rigo M. (eds) Developments in Language Theory, DLT 2017, Lecture Notes in Computer Science, vol 10396. doi:10.1007/978-3-319-62809-7_23
  211. Vincent Pilaud, Brick polytopes, lattice quotients, and Hopf algebras, preprint arXiv:1505.07665 (A000108, A078920, A003319, A001181, A033282)
  212. Vincent Pilaud, V Pons, Permutrees, arXiv preprint arXiv:1606.09643, 2016
  213. V. Pilaud, J. Rué, Analytic combinatorics of chord and hyperchord diagrams with k crossings, arXiv preprint arXiv:1307.6440, 2013
  214. Khodabakhsh Hessami Pilehrood and Tatiana Hessami Pilehrood, Vacca-type series for values of the generalized-Euler-constant function and its derivative (2008); arXiv:0808.0410
  215. K. H. Pilehrood, T. H. Pilehrood, Jacobi Polynomials and Congruences Involving Some Higher-Order Catalan Numbers and Binomial Coefficients, J. Int. Seq. 18 (2015) 15.11.7
  216. Deanna Pineau, Math-Aware Search Engines: Physics Applications and Overview, arXiv preprint arXiv:1609.03457, 2016.
  217. Sandra Pinelas, Paolo Emilio Ricci, On Sheffer polynomial families, 4open (2019), Vol. 2, No. 4, 1-9. doi:10.1051/fopen/2019004
  218. S. Pion, De la géométrie algorithmique au calcul géométrique, Ph.D thesis, Université de Nice Sophia-Antipolis, 1999. (PostScript, PDF)
  219. T. Pisanski, D. Schattschneider and B. Servatius, Applying Burnside's Lemma to a One-Dimensional Escher Problem, Mathematics Magazine, vol. 79, #3, 167-180.
  220. C. de Jesus Pita Ruiz Velasco, Convolution and Sulanke Numbers, JIS 13 (2010) 10.1.8
  221. C. Pita, On s-Fibonomials, J. Int. Seq. 14 (2011) # 11.3.7
  222. C. J. Pita Ruiz Velasco, Sums of Products of s-Fibonacci Polynomial Sequences, J. Int. Seq. 14 (2011) # 11.7.6
  223. Claudio de Jesus Pita Ruiz Velasco, A Note on Fibonacci & Lucas and Bernoulli & Euler Polynomials, Journal of Integer Sequences, Vol. 15 (2012), Article #12.2.7
  224. Pita Ruiz V., Claudio de J., Some number arrays related to Pascal and Lucas triangles. J. Integer Seq. 16 (2013), no. 5, Article 13.5.7, 34 pp.
  225. Pita Ruiz V., Claudio de J., Some weighted sums of powers of Fibonacci polynomials. Integers 13 (2013), Paper No. A60, 19 pp.
  226. Pita Ruiz V., Claudio de J., Generalized Stirling numbers and hyper-sums of powers of binomial coefficients. Electron. J. Combin. 21 (2014), no. 1, Paper 1.10, 39 pp.
  227. Jim Pitman and Wenpin Tang, Regenerative random permutations of integers, arXiv:1704.01166, [math.PR], 2017.
  228. Irene Pivotto, Gordon Royle, Highly-connected planar cubic graphs with few or many Hamilton cycles, arXiv:1901.10683 [math.CO], 2019. (A006791, A007021)
  229. Robert Piziak, Remarks on some papers of Flachsmeyer and Katrnoška, Baylor University (2019). doi:10.13140/RG.2.2.11485.05606
  230. M. Planat, Twelve-dimensional Pauli group contextuality with eleven rays, Arxiv preprint arXiv:1201.5455, 2012
  231. M. Planat, Twelve-dimensional Pauli group contextuality, 2012, PDF
  232. M. Planat, A. Giorgetti, F. Holweck, M. Saniga, Quantum contextual finite geometries from dessins d'efants, arXiv:1310.4267 (2013-2015)
  233. Michel Planat, Patrick Sole, arXiv:1109.6489 Efficient prime counting and the Chebyshev primes. Also Hindawi Publishing Corporation, Journal of Discrete Mathematics, Volume 2013, Article ID 491627, 11 pages, doi:10.1155/2013/491627.
  234. Michel Planat, Patrick Solé, Improving Riemann prime counting, arXiv preprint arXiv:1410.1083, 2014
  235. David J. Platt, T Trudgian, On the sum of two squares and at most two powers of 2, arXiv preprint arXiv:1610.01672, 2016
  236. V. Pletser, Conjecture on the value of Pi(10^26), the number of primes less than 10^26, arXiv preprint arXiv:1307.4444, 2013
  237. V. Pletser, Congruence conditions on the number of terms in sums of consecutive squared integers equal to squared integers, arXiv preprint arXiv:1409.7969, 2014
  238. V. Pletser, Finding all squared integers expressible as the sum of consecutive squared integers using generalized Pell equation solutions with Chebyshev polynomials, arXiv preprint arXiv:1409.7972, 2014
  239. V. Pletser, General solutions of sums of consecutive cubed integers equal to squared integers, arXiv preprint arXiv:1501.06098, 2015
  240. Vladimir Pletser, Number of terms, first term and square root of sums of consecutive cubed integers equal to integer squares, Research Gate, 2015; PDF
  241. V. Pletser, Fundamental solutions of the Pell equation X^2-(sigma^4-delta^4)Y^2=deleta^4 for the first 45 solutions of the sums of consecutive cubed integers equalling integer squares 2015, PDF
  242. S. Plouffe, Approximations de séries génératrices et quelques conjectures, Master's Thesis, Univ. du Québec à Montréal, August, 1992. There is a separate page for the associated formulae.
  243. S. Plouffe, Un methode pour obtenir la fonction generatrice algebrique d'une serie, FPSAC, Florence, June 1993.
  244. Simon Plouffe, "The Computation of Certain Numbers Using a Ruler and Compass", J. Integer Sequences, Volume 1, 1998, Article 98.1.3.
  245. Simon Plouffe, Identities and approximations inspired from Ramanujan notebooks, III</a>, 2009.
  246. Simon Plouffe, A search for a mathematical expression for mass ratios using a large database,, also; 2012.
  247. S. Plouffe, On the values of the functions ... [zeta and Gamma] ..., arXiv preprint arXiv:1310.7195, 2013
  248. S. Plouffe, The many faces of the polygamma function PDF, 2016
  249. Simon Plouffe, Primes as sums of irrational numbers, Preprint. 2016;
  250. Simon Plouffe, A set of formulas for primes, arXiv:1901.01849 [math.NT], 2019. (A000058)
  251. Simon Plouffe, π, the primes and the Lambert W-function (2), Bulletin of the Derive User Group (2019) Newsletter #116, 5-16. PDF
  252. F. Pluvinage, Developing problem solving experiences in practical action projects, The Mathematics Enthusiast, ISSN 1551-3440, Vol. 10, nos.1&2, pp. 219-244; PDF
  253. Ricardo A. Podestá, New identities for binary Krawtchouk polynomials, binomial coefficients and Catalan numbers, arXiv preprint arXiv:1603.09156, 2016
  254. K. Podnieks, Digits of pi: limits to the seeming randomness, arXiv preprint arXiv:1411.3911, 2014
  255. Md Masbaul Alam Polash, M. A. Hakim Newton, Abdul Sattar, Constraint-directed search for all-interval series, Constraints, July 2017, Volume 22, Issue 3, pp 403–431; doi:10.1007/s10601-016-9261-y
  256. Nikolay L. Poliakov, Note on level r consensus, arXiv:1606.04816 [q-fin.EC]
  257. Alberto Policriti and Alexandru I. Tomescu, Counting extensional acyclic digraphs, Information Processing Letters, Volume 111 Issue 16, August 2011 , pp. 305-315.
  258. P. Pollack, C. Pomerance, Some problems of Erdos on the sum-of-divisors function, For Richard Guy on his 99th birthday: May his sequence be unbounded, Trans. Am. Math. Soc. B 3 (2016) 1-26 doi:10.1090/btran/10.
  259. PAUL POLLACK AND VLADIMIR SHEVELEV, On perfect and near-perfect numbers, J. Number Theory 132 (2012), 3037--3046;
  260. Pollack, Paul; Treviño, Enrique. The Primes that Euclid Forgot. Amer. Math. Monthly 121 (2014), no. 5, 433--437. MR3193727.
  261. M. Pollanen, UNIFORM EQUIPARTITION TEST BOUNDS FOR MULTIPLY SEQUENCES, International Journal of Pure and Applied Mathematics, Volume 72 No. 4 2011, 515-526;
  262. Burkard Polster and Marty Ross, Marching in squares, arXiv preprint arXiv:1503.04658, 2015.
  263. D. H. J. Polymath, arXiv:1002.0374 Density Hales-Jewett and Moser numbers.
  264. PolyMath REU Convex Geometries Collaboration: Kira Adaricheva, Madina Bolat, Gent Gjonbalaj, Brandon Amerine, J. Alexandria Behne, Evan Daisy, Alexander Frederiksen, Ayush Garg, Zachary King, Grace Ma, Michelle Olson, Rohit Pai, Junewoo Park, Cat Raanes, Sean Riedel, Joseph Rogge, Raviv Sarch, James Thompson, Fernanda Yepez-Lopez, Stephanie Zhou, Convex geometries representable by at most 5 circles on the plane, arXiv:2008.13077 [math.CO], 2020. An OEIS (On-line Encyclopedia of Integer Sequences) submission on the number of non-isomorphic antimatroids by Przemysław Uznański [10] served as the starting point for our project. The algorithm was developed around 2013, in the framework of enumerating anti-matroids in the On-line Encyclopedia of Integer Sequences (OEIS). The existing code was enhanced for computing the implicational basis of each geometry and its convex dimension.
  265. Maxim V. Polyakov, Kirill M. Semenov-Tian-Shansky, Alexander O. Smirnov, Alexey A. Vladimirov, Quasi-Renormalizable Quantum Field Theories, arXiv:1811.08449 [hep-th], 2018. (A000108, A098777)
  266. C. Pomerance, Divisors of the middle binomial coefficient, Amer. Math. Monthly, 112 (2015), 636-644.
  267. Carl Pomerance, Simon Rubinstein-Salzedo, Cyclotomic Coincidences, arXiv:1903.01962 [math.NT], 2019. (A206225)
  268. C. Pomerance and H.-S. Yang, On untouchable numbers and related problems,, 2012.
  269. C. Pomerance and H.-S. Yang, Variant of a theorem of Erdos on the sum-of-proper-divisors function,, 2012.
  270. Klaus Pommerening, The Indecomposable Solutions of Linear Congruences, arXiv:1703.03708, 2017.
  271. M. Poneti, V. Vajnovszki, doi:10.1016/j.ejc.2009.03.028, Generating restricted classes of involutions, Bell and Stirling permutations, Eur. J. Combinat. 31 (2) (2010) 553-564
  272. P. Pongsriiam, Relatively Prime Sets, Divisor Sums, and Partial Sums, arXiv preprint arXiv:1306.4891, 2013 and J. Int. Seq. 16 (2013) #13.9.1
  273. Prapanpong Pongsriiam, Kittipong Subwattanachai, Exact Formulas for the Number of Palindromes up to a Given Positive Integer, Intl. J. of Math. Comp. Sci. (2019) 14:1, 27-46. PDF (A002113)
  274. A. Pönitz, Über die Methode zur Konstruktion von Algorithmen für die Berechnung von Invarianten in endlichen ungerichteten Hypergraphen, Ph.D Thesis (2004)
  275. Sankar Ponnapalli, V. A., and P. V. Y. Jayasree Pappu. "An investigation of fractal antenna arrays for side lobe reduction with a fractal distribution of current." Advances in Computing, Communications and Informatics (ICACCI), 2015 International Conference on. IEEE, 2015.
  276. V. A. Sankar Ponnapalli and V. Y. Jayasree Pappu, Design of Octagonal Fractal Array Antenna for Side Lobe Reduction with Morse-Thue Fractal Density Tapering Technique, Preprint, 2016.
  277. V A Sankar Ponnapalli, P V Y Jayasree, A Three Valued Morse-Thue Fractal Tapering for Thinning of Fractal Array Antennas, Journal of Science and Technology: Issue on Information and Communications Technology, Vol. 2, No. 1, August 2016.
  278. Luca Terzio Pontiggia, Computational methods in string and field theory, doctoral dissertation, Univ. of the Witwatersrand, Johannesburg, 2018. PDF (A090045)
  279. B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156 (PostScript, PDF). (Although the Encyclopedia is not mentioned in the final version, this paper was born when I wrote the beginning of sequence A007678 on the blackboard in the Commons Room at AT&T Bell Labs and appealed to people to extend it.)
  280. J. Pope, D. Sonnier, A linear solution to the n-Queens problem using vector spaces, Journal of Computing Sciences in Colleges, Volume 29 Issue 5, May 2014 Pages 77-83.
  281. Oleg Posnansky, Ruiwang Huang, N. Jon Shah, The truncated Levy-flight process: Application to the random spin phase change in non-linear magnetic fields, Physica A: Statistical Mechanics and its Applications, Volume 370, Issue 2, 15 October 2006, Pages 553-564.
  282. A. Postnikov and R. P. Stanley, Deformations of Coxeter hyperplane arrangements, Journal of Combinatorial Theory, Series A 91 (2000), no. 1-2, 544-597. (Special issue dedicated to G.-C. Rota.)
  283. William Poundstone, Are You Smart Enough to Work at Google?: Trick Questions, Zen-like Riddles, Insanely Difficult Puzzles, and Other Devious Interviewing Techniques You Need to Know to Get a Job Anywhere in the New Economy, Little, Brown and Company, 2012.
  284. Maurice Pouzet, The Profile of relations (2007), arXiv:math/0703211.
  285. Pouzet, Maurice; Thiéry, Nicolas M. Some relational structures with polynomial growth and their associated algebras I: Quasi-polynomiality of the profile. Electron. J. Combin. 20 (2013), no. 2, Paper 1, 35 pp.
  286. Geoffrey Powell, Symmetric powers, indecomposables and representation stability, arXiv:1809.08781 [math.AT], 2018. (A045412, A100661)
  287. S. C. Power, arXiv:math.OA/0005110 Approximately finitely acting operator algebras, J. Funct. Anal. 189 (2002), no. 2, 409-468.
  288. A. Prasad, Equivalence classes of nodes in trees and rational generating functions, arXiv preprint arXiv:1407.5284, 2014
  289. A. Prasad, Representation Theory, A Combinatorial Viewpoint, Cambridge Studies in Advanced Mathematics, 2014.
  290. J. S. Pratt, Universality in the entanglement structure of ferromagnets (2004), arXiv:quant-ph/0411125.
  291. V. R. Pratt, Chu Spaces: Complementarity and Uncertainty in Rational Mechanics, Course notes, TEMPUS summer school, Budapest, July 1994.
  292. Emmanuel Preissmann, "A Self-Indexed Sequence", J. Integer Sequences, Volume 8, 2005, Article 05.3.5.
  293. Louis-François Préville-Ratelle and Xavier Viennot, An extension of Tamari lattices, Discrete Mathematics & Theoretical Computer Science, FPSAC 2013 Paris, France, DMTCS Proc. AS, 2013 [Mentions A000139. A version on the arXiv, arXiv:1406:3787, 2014, with the same title, does not mention the OEIS.]
  294. Louis-François Préville-Ratelle and Xavier Viennot, The enumeration of generalized Tamari intervals, Trans. Amer. Math. Soc. 369 (2017), 5219-5239. doi:10.1090/tran/7004
  295. Thomas B. Preuβer and Matthias R. Engelhardt, Putting Queens in Carry Chains, No27, Journal of Signal Processing Systems, Volume 88, Issue 2, August 2017, p. 185-201. doi:10.1007/s11265-016-1176-8
  296. Andrew Elvey Price, Wenjie Fang, Michael Wallner, Asymptotics of Minimal Deterministic Finite Automata Recognizing a Finite Binary Language, 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020) Leibniz International Proceedings in Informatics (LIPIcs) Vol. 159, 11:1-11:13. doi:10.4230/LIPIcs.AofA.2020.11 (A331120)
  297. Andrew Elvey Price, Alan D. Sokal, Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials, arXiv:2001.01468 [math.CO], 2020. (A000311, A001498, A008299, A008517, A112007, A112493, A134685, A134991, A137375, A181996, A201637, A269939, A288874, A298673) This work has benefited greatly from the existence of the On-Line Encyclopedia of Integer Sequences. We warmly thank Neil Sloane for founding this indispensable resource, and the hundreds of volunteers for helping to maintain and expand it.
  298. R. Pries and C. Weir, The Ekedahl-Oort type of Jacobians of Hermitian curves, arXiv preprint arXiv:1302.6261, 2013
  299. J.-B. Priez, A lattice of combinatorial Hopf algebras, Application to binary trees with multiplicities, arXiv preprint arXiv:1303.5538, 2013. Published in FPSAC 2013 Paris, France DMTCS Proc. AS, 2013, 1167-1179; PDF
  300. J.-B. Priez, A. Virmaux, Non-commutative Frobenius characteristic of generalized parking functions: Application to enumeration, arXiv preprint arXiv:1411.4161, 2014
  301. Raul Prisacariu, Generating k-Pell Infinite Series Using Whittaker's Formula. PDF (A000129)
  302. U. Priss, Lattice-based Information Retrieval, Knowledge Organization, Vol. 27, 3, 2000, p. 132-142.
  303. Robert A. Proctor, Let's Expand Rota's Twelvefold Way For Counting Partitions! (2006), arXiv:math.CO/0606404.
  304. Robert A. Proctor and Matthew J. Willis, Convexity of tableau sets for type A Demazure characters (key polynomials), parabolic Catalan numbers, arXiv:1706.03094 [math.CO], 2017. [On p. 18, notes that the OEIS was used to find relevant literature.]
  305. Robert A. Proctor, MJ Willis, Parabolic Catalan numbers count flagged Schur functions; Convexity of tableau sets for Demazure characters, arXiv preprint arXiv:1612.06323, 2016
  307. H. Prodinger, Generating functions related to partition formulae for Fibonacci Numbers, JIS 11 (2008) 08.1.8.
  308. Helmut Prodinger, Generating functions for a lattice path model introduced by Deutsch, arXiv:2004.04215 [math.CO], 2020. (A001764)
  309. Helmut Prodinger, Retakh's Motzkin paths and some combinatorial comments, ECA 1:1 (2021) Article S2R4.
  310. Helmut Prodinger, Counting ternary trees according to the number of middle edges and factorizing into (3/2)-ary trees, arXiv:2009.06793 [math.CO], 2020. (A120986)
  311. Helmut Prodinger, Summing a family of generalized Pell numbers, arXiv:2010.14321 [math.NT], 2020.
  312. Helmut Prodinger, Sarah J. Selkirk, Sums of squares of Tetranacci numbers: A generating function approach, arXiv:1906.08336 [math.NT], 2019. (A000078)
  313. H. Prodinger and T. A. Tshifhumulo, On q-Olivier functions, Annals of Combinatorics, 6 (2002), no. 2, 181-194.
  314. J. Propp, Integrability, Exact Solvability and Algebraic Combinatorics: A Three-Way Bridge?, presented in the Workshop on Combinatorics and Integrable Models, Canberra, 2002.
  315. J. Propp, Tilings, Chapter 9 in Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, pages 541-588.
  316. J. Propp, Lessons I learned from Richard Stanley, arXiv preprint arXiv:1501.00719, 2015
  317. J. Propp and D. Ullman, On the Cookie Game, International Journal of Game Theory, volume 20 (1992), pages 313-324.
  318. Nicholas Proudfoot, Max Wakefield, and Ben Young, Intersection Cohomology of the Symmetric Reciprocal Plane, Preprint,, 2015. ["All three authors would like to acknowledge the On-Line Encyclopedia of Integer Sequences [Slo14], without which this project would have been very difficult."]
  319. Nicholas Proudfoot and Ben Young, Configuration spaces, FSop-modules, and Kazhdan-Lusztig polynomials of braid matroids, arXiv:1704.04510 [math.RT], 2017.
  320. Nicholas Proudfoot, Ben Young, Yuan Xu, The Z-polynomial of a matroid, arXiv:1706.05575 [math.CO], 2017.
  321. Mihai Prunescu, Self-similar carpets over finite fields (2007), arXiv:0708.0899.
  322. Jozef H. Przytycki, History of Knot Theory (2007), arXiv:math/0703096.
  323. W. Pu, J. Choi, E. Amir, Lifted Inference On Transitive Relations, in Workshops at the Twenty-Seventh AAAI Conference on Statistical Relational Artificial Intelligence, 2013.
  324. Lara Pudwell, Digit Reversal Without Apology (2005), arXiv:math/0511366.
  325. Lara Pudwell, Enumeration schemes for permutations avoiding barred patterns, El. J. Combin. 17 (1) (2010) R29.
  326. L. Pudwell, Pattern avoidance in trees (slides from a talk, mentions many sequences),, 2012.
  327. L. Pudwell, Avoiding an Ordered Partition of Length 3, 2013;
  328. L. K. Pudwell, Ascent sequences and the binomial convolution of Catalan numbers, arXiv preprint arXiv:1408.6823, 2014
  329. L. Pudwell, Pattern-avoiding ascent sequences, Slides from a talk, 2015;
  330. Lara Pudwell, On the distribution of peaks (and other statistics), 16th International Conference on Permutation Patterns, Dartmouth College, 2018. PDF (A001263, A091156, A091894, A092107, A236406)
  331. Lara Pudwell, From permutation patterns to the periodic table, Valparaiso University (2019). PDF Also Notices Amer. Math. Soc., 67:7 (2020), 994-1001. (A168380)
  332. L. Pudwell, A. Baxter, Ascent sequences avoiding pairs of patterns, 2014.
  333. Lara Pudwell, Nathan Chenette, Manda Riehl, Statistics on Hypercube Orientations, AMS Special Session on Experimental and Computer Assisted Mathematics, Joint Mathematics Meetings (Denver 2020). PDF (A001787, A001788, A061301)
  334. Pudwell, Lara; Scholten, Connor; Schrock, Tyler; Serrato, Alexa doi:10.1155/2014/316535 Noncontiguous pattern containment in binary trees. ISRN Comb. 2014, Article ID 316535, 8 p. (2014).
  335. Lara Pudwell, Rebecca Smith, Two-stack-sorting with pop stacks, arXiv:1801.05005 [math.CO], 2018. (A224232)
  336. Sílvia Casacuberta Puig, On the divisibility of binomial coefficients, 2018. PDF (A290290, A290203)
  337. Yash Puri and Thomas Ward, "Arithmetic and Growth of Periodic Orbits", J. Integer Sequences, Volume 4, 2001, Article 01.2.1.
  338. Robert James Purser, Mobius Net Cubed-Sphere Gnomonic Grids, U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service, National Centers for Environmental Protection, 2018. doi:10.25923/d9rn-fd18 (A008958)
  339. Pushkarev, I. A.; Byzov, V. A. Donaghey's transformation: an elementary approach. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 411 (2013), Teoriya Predstavlenii, Dinamicheskie Sistemy, Kombinatornye Metody. XXII, 148--177, 243; translation in J. Math. Sci. (N. Y.) 196 (2014), no. 2, 199-215
  340. B. Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732, 2012
  341. The Dutch magazine Pythagoras ( currently (in 2015) has a series of articles about number sequences, many of which mention the OEIS. Four parts have appeared so far: Een Lexicon vol Getallen ["A Dictionary of Numbers"] (Sept. 2015), Getallenplantjes ["Number plants" (?)] (Oct. 2015), Driehoeksgetallen ["Triangular numbers"] (Nov. 2015), Een bizarre rij [A bizarre sequence] (Dec. 2015),
  342. Pythagoras, Een Eigen Rij - Uitslag Prijsvraag, Nummer 6, Juni 2016, pp. 20-21.
  343. Pythagoras in 2016 had a series of illustrations on the back covers showing sequences from the OEIS. For an example see the January 2016 issue,

About this page

  • This is part of the series of OEIS Wiki pages that list works citing the OEIS.
  • Additions to these pages are welcomed.
  • But if you add anything to these pages, please be very careful — remember that this is a scientific database. Spell authors' names, titles of papers, journal names, volume and page numbers, etc., carefully, and preserve the alphabetical ordering.
  • If you are unclear about what to do, contact one of the Editors-in-Chief before proceeding.
  • Works are arranged in alphabetical order by author's last name.
  • Works with the same set of authors are arranged by date, starting with the oldest.
  • The full list of sections is: A Ba Bi Ca Ci D E F G H I J K L M N O P Q R Sa Sl T U V W X Y Z.
  • For further information, see the main page for Works Citing OEIS.