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# CiteP

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## References

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. Martin Paech, Numerische und algebraisch-graphentheoretische Algorithmen für korrelierte Quantensysteme, Dissertation, Hannover: Fakultät für Mathematik und Physik der Leibniz Universität, 2015.
4. 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.
5. 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).
6. 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).
7. 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
8. Don N. Page, Religious and Scientific Faith in Simplicity (2008); arXiv:0811.0630
9. David Pagni, Building buildings with triangular numbers, AMATYC Review (vol. 27 no. 2 spring 2006, pp. 56-65).
10. 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.
11. 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
12. 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
13. 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
14. I. Pak, Partition Identities and Geometric Bijections, Proc. Amer. Math. Soc. 132 (2004), 3457-3462.
15. Igor Pak, History of Catalan numbers, arXiv:1408.5711, 2014.
16. 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)
17. I. Pak and G. Panova, Unimodality via Kronecker products, arXiv preprint arXiv:1304.5044, 2013
18. I. Pak, G. Panova, E. Vallejo, Kronecker products, characters, partitions, and the tensor square conjectures, arXiv:1304.0738, 2013
19. I. Pak, A. Soffer, On Higman's k(U_n(F_q)) conjecture, arXiv preprint arXiv:1507.00411, 2015
20. Apisit Pakapongpun, Thomas Ward, Functorial orbit counting (2009) arXiv:0901.2646 and JIS 12 (2009) 09.2.4
21. 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
22. M. B. Paksoy, Derived Ramanujan Primes: R'_{N}, arXiv preprint arXiv:1210.6991, 2012
23. S. Palasek, Non-Cooperativity in Bayesian Social Learning, arXiv preprint arXiv:1407.0519, 2014
24. Sushma Palimar and B. R. Shankar, Mersenne Primes in Real Quadratic Fields, Journal of Integer Sequences, Vol. 15 (2012), #12.5.6.
25. J. M. Pallo, On the listing and random generation of hybrid binary trees, International Journal of Computer Mathematics, 50, 1994, 135-145.
26. 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.
27. Jean Marcel Pallo, Weak associativity and restricted rotation, Information Processing Letters, Volume 109, Issue 10, 30 April 2009, Pages 514-517.
28. M. Palmacci, Escher's Problem and Numerical Sequences, (2006)
29. M. G. Palomo, Latin polytopes, arXiv preprint arXiv:1402.0772, 2014
30. Hao Pan, Z.-W. Sun, Consecutive primes and Legendre symbols, arXiv preprint arXiv:1406.5951, 2014
31. J. Pan, Multiple Binomial Transforms and Families of Integer Sequences, J. Int. Seq. 13 (2010), 10.4.2.
32. 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.
33. 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.
34. 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.
35. Ran Pan, Block patterns in permutations and words and generalized clusters, Ph. D. Dissertation, Univ. Calif. San Diego, 2016.
36. R. Pan, J. B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 (2016)
37. 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
38. D. Panario, M. Sahin, Q. Wang, A family of Fibonacci-like conditional sequences, INTEGERS, Vol. 13, 2013, #A78.
39. D. Panario, M. Sahin, Q. Wang, W. Webb, General conditional recurrences, Applied Mathematics and Computation, Volume 243, 15 September 2014, Pages 220-231.
40. A. Panayotopoulos and P. Tsikouras, "Meanders and Motzkin Words", J. Integer Sequences, Volume 7, 2004, Article 04.1.2.
41. 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.
42. 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)
43. Ram Krishna Pandey, "On Some Magnified Fibonacci Numbers Modulo a Lucas Number" , Journal of Integer Sequences, Vol. 16 (2013), #13.1.7.
44. 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.
45. 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.
46. Jay Pantone, The Enumeration of Permutations Avoiding 3124 and 4312, arXiv preprint arXiv:1309.0832, 2013
47. D. Panyushev, On the orbits of a Borel subgroup in abelian ideals, arXiv preprint arXiv:1407.6857, 2014
48. 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.
49. 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.
50. G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
51. Daniel Pareja, Prime Number Races, PDF
52. D. Parisse, The Tower of Hanoi and the Stern-Brocot Array, Thesis, Ludwig-Maximilians-Universitaet Munich, August 1997.
53. Boram Park and Seonjeong Park, Shellable posets arising from even subgraphs of a graph, arXiv:1705.06423 [math.CO], 2017.
54. Donghwi Park, Space-state complexity of Korean chess and Chinese chess, arXiv preprint arXiv:1507.06401, 2015
55. 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.
56. 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.
57. 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
58. Park, Youngja, and SeungKyung Park. "Enumeration of generalized lattice paths by string types, peaks, and ascents." Discrete Mathematics 339.11 (2016): 2652-2659.
59. 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.
60. 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).
61. 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)
62. 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)
63. 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)
64. 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
65. 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
66. 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.
67. Robert Parviainen, "Parametric Production Matrices and Weighted Succession Rules: a Dyck Path Example", J. Integer Sequences, Volume 10, 2007, Article 07.6.1.
68. Robert Parviainen, Some bijections on set partitions (2007), arXiv:0710.1132.
69. A. Pathak, Non-Hermitian quantum gates are more common than Hermitian quantum gates, arXiv preprint arXiv:1309.4037, 2013
70. 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
71. 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; http://www.ijsres.com/2014/vol-1_issue-6/paper_8.pdf
72. N. Patson, Pisano period and permutations of n X n matrices, Australian Math. Soc. Gazette, 2007.
73. Paukner, M., Pepin, L., Riehl, M., and Wieser, J., Pattern Avoidance in Task-Precedence Posets, arXiv:1511.00080
74. Shubhankar Paul, Ten Problems of Number Theory, International Journal of Engineering and Technical Research (IJETR), ISSN: 2321-0869, Volume-1, Issue-9, November 2013
75. 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; http://erpublication.org/admin/vol_issue1/upload%20Image/IJETR012013.pdf
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79. J. Pawlewicz, Counting Square-Free Numbers, Arxiv preprint arXiv:1107.4890, 2011
80. J. L. Pe, Ana's Golden Fractal.
81. J. L. Pe, On a Generalization of Perfect Numbers, To appear in The Journal of Recreational Mathematics 31(3).
82. J. L. Pe, Fractal dimension, primes and the persistence of memory, Adv. Compl. Systems 6(2) (2003) 241-249
83. Joseph L. Pe, The 3x+1 fractal, Computers & Graphics, Volume 28, Issue 3, June 2004, Pages 431-435.
84. Paul A. Pearce and Alessandra Vittorini-Orgeas, Yang-Baxter Solution of Dimers as a Free-Fermion Six-Vertex Model. arXiv:https://arxiv.org/abs/1612.09477, 2017.
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86. Paul Peart and Wen-Jin Woan, "Dyck Paths With No Peaks At Height k", J. Integer Sequences, Volume 4, 2001, Article 01.1.3.
87. J. Peebles, Cap Set Bounds and Matrix Multiplication, Senior Thesis, Harvey Mudd College, 2013; http://www.math.hmc.edu/seniorthesis/archives/2013/jpeebles/jpeebles-2013-thesis-poster.pdf
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90. 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.
91. 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.
92. Tiago P. Peixoto, Bayesian stochastic blockmodeling, arXiv:1705.10225 [stat.ML], 2017.
93. 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.
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139. Kolosov Petro, Relation between Pascal’s triangle and hypercubes, 2018. PDF (A007318)
140. Ian Petrow, MP Young, A generalized cubic moment and the Petersson formula for newforms, arXiv preprint arXiv:1608.06854, 2016
141. V. H. Pettersson, Enumerating Hamiltonian Cycles, The Electronic Journal of Combinatorics, 21 (4) 2014, #P4.7.
142. Ville Pettersson, Graph Algorithms for Constructing and Enumerating Cycles and Related Structures, Preprint 2015, https://aaltodoc.aalto.fi/bitstream/handle/123456789/17688/isbn9789526063652.pdf?sequence=1
143. Robertas Petuchovas, Asymptotic analysis of the cyclic structure of permutations, arXiv preprint arXiv:1611.02934, 2016
144. 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.
145. J. L. Pfaltz, Partitions of 2^n, Congressus Numerantium 109:3-12, 1995.
146. 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.
147. 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.
148. Götz Pfeiffer, "Counting Transitive Relations", J. Integer Sequences, Volume 7, 2004, Article 04.3.2.
149. 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.
150. Hugo Pfoertner, Uniform Illumination of a Sphere
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155. Phakhinkon Phunphayap, Prapanpong Pongsriiam, Reciprocal sum of palindromes, arXiv:1803.00161 [math.CA], 2018. (A002113, A002385, A002779)
156. 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)
157. Steven T. Piantadosi, Problems in the philosophy of mathematics: A view from cognitive science, preprint.
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