This site is supported by donations to The OEIS Foundation.


From OeisWiki

Jump to: navigation, search



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 F.
  • 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. V. Fack, S. Lievens and J. Van der Jeugt, On rotation distance between binary coupling trees and applications for 3nj-coefficients, Comput. Phys. Commun., 119 (1999) 99-114.
  2. V. Fack, S. Lievens and J. Van der Jeugt, On the diameter of the rotation graph of binary coupling trees. Discrete Mathematics 245 (2002) 1-18.
  3. Vinicius Facó, D Marques, Tribonacci Numbers and the Brocard-Ramanujan Equation, - Journal of Integer Sequences, Vol. 19, 2016, #16.4.4.
  4. P. Fahr, C. M. Ringel, A partition number for Fibonacci Numbers, JIS 11 (2008) 08.1.4.
  5. Philipp Fahr and Claus Michael Ringel, Categorification of the Fibonacci Numbers Using Representations of Quivers, JIS 15 (2012) 12.2.1
  6. N.-E. Fahssi, The polynomial triangles revisited, Arxiv preprint arXiv:1202.0228, 2012
  7. N.-E. Fahssi, A Systematic Study of Polynomial Triangles, Electronic Journal of Combinatorics, 2012.
  8. N.-E. Fahssi, The many aspects of polynomial triangles, Conference on Discrete Mathematics and Computer Science, Algeria, Sidi Bel Abbès, Nov 15-19, 2015; Recits Laboratory, Faculty of Mathematics, USTHB;; pages 147-150.
  9. G. Failla, C. Peterson, R. Utano, Algorithms and basic asymptotics for generalized numerical semigroups in N^d, Semigroup Forum, Jan 31 2015, doi:10.1007/s00233-015-9690-8
  10. Sergio Falcon, On the k-Lucas numbers, Int. J. Cont. Math. Sci. 6 (2011) 1039-1050
  11. S. Falcon, On the Lucas triangle and its relationship with the k-Lucas numbers, Journal of Mathematical and Computational Science, 2 (2012), No. 3, 425-434. Available online at
  12. S. Falcon, Generalized Fibonacci Sequences Generated from a $ k $--Fibonacci Sequence, Journal of Mathematics Research Vol. 4, No. 2; April 2012;
  13. Sergio Falcon, Catalan transform of the K-Fibonacci sequence, Commun. Korean Math. Soc. 28 (2013), No. 4, pp. 827-832; doi:10.4134/CKMS.2013.28.4.827.
  14. S. Falcon, Relationships between Some k-Fibonacci Sequences, Applied Mathematics, 2014, 5, 2226-2234; doi:10.4236/am.2014.515216
  15. S. Falcon, On The Generating Functions of the Powers of the K-Fibonacci Numbers, Scholars Journal of Engineering and Technology (SJET), 2014; 2 (4C):669-675;
  16. S. Falcon, On the k-Jacobsthal Numbers, American Review of Mathematics and Statistics, March 2014, Vol. 2, No. 1, pp. 67-77, ISSN 2374-2348 (Print) 2374-2356 (Online);
  17. S. Falcon, Iterated Binomial Transforms of the k-Fibonacci Sequence, British Journal of Mathematics & Computer Science, 4 (22): 2014.
  18. S. Falcon, On the Sequences of Products of Two k-Fibonacci Numbers, American Review of Mathematics and Statistics, March 2014, Vol. 2, No. 1, pp. 111-120.
  19. S. Falcon, Generalized (k, r)–Fibonacci Numbers, Gen. Math. Notes, Vol. 25, No. 2, December 2014, pp.148-158;
  20. Sergio Falcon, The k–Fibonacci difference sequences, Chaos, Solitons & Fractals, Volume 87, June 2016, Pages 153–157.
  21. Sergio Falcon, On the complex k-Fibonacci numbers, Cogent Mathematics, (2016), 3: 1201944; doi:10.1080/23311835.2016.1201944
  22. Sergio Falcon, Angel Plaza, On k-Fibonacci numbers of arithmetic indexes, Applied Mathematics and Computation, Volume 208, Issue 1, 1 February 2009, Pages 180-185.
  23. Sergio Falcon, Angel Plaza, On k-Fibonacci sequences and polynomials and their derivatives, Chaos, Solitons & Fractals, Volume 39, Issue 3, 15 February 2009, Pages 1005-1019.
  24. Sergio Falcon, Angel Plaza, The metallic ratios as limits of complex valued transformations, Chaos, Solitons & Fractals, Volume 41, Issue 1, 15 July 2009, Pages 1-13.
  25. Sergio Falcon, Angel Plaza, k-Fibonacci sequences modulo m, Chaos, Solitons & Fractals, Volume 41, Issue 1, 15 July 2009, Pages 497-504.
  26. Victor Falgas-Ravry and Emil R. Vaughan, On applications of Razborov's flag algebra calculus to extremal 3-graph theory, Arxiv preprint arXiv:1110.1623, 2011
  27. Falgas-Ravry, Victor; Vaughan, Emil R. Applications of the semi-definite method to the Turán density problem for 3-graphs. Combin. Probab. Comput. 22 (2013), no. 1, 21-54. doi:10.1017/S0963548312000508
  28. Xin Fang and Ghislain Fourier, Torus fixed points in Schubert varieties and Genocchi numbers, arXiv:1504.03980.
  29. Reza Farhadian, A New Conjecture On the primes, Preprint, 2016;
  30. Bakir Farhi, A Study of a Curious Arithmetic Function Journal of Integer Sequences, Vol. 15 (2012), #12.3.1.
  31. Michael Farina and Armando Grez, New Upper Bounds on the Distance Domination Numbers of Grids, Rose-Hulman Undergraduate Mathematics Journal, Volume 17, No. 2, Article 7, Fall 2016.
  32. G. Farkas, G. Kallos and G. Kiss, Large primes in generalized Pascal triangles Acta Univ. Sapientiae, Informatica, 3, 2 (2011) 158-171;
  33. Elin Farnell, Puzzle Pedagogy: A Use of Riddles in Mathematics Education, PRIMUS, July 2016, pp. 202-211; doi:10.1080/10511970.2016.1195465
  34. M. Farrokhi D. G., "Some Remarks On the Equation Fn = kFm In Fibonacci Numbers", J. Integer Sequences, Volume 10, 2007, Article 07.5.7.
  35. Joseph A. Farrow and Arthur E. Lipstein, From 4d Ambitwistor Strings to On Shell Diagrams and Back, arXiv:1705.07087v1 [hep-th], 2017. (OEIS only cited in version 1) ["We thank Daniele Dorigoni for identifying this function using The On-Line Encyclopedia of Integer Sequences"]
  36. Nazim Fatès, Remarks on the Cellular Automaton Global Synchronisation Problem, in Cellular Automata and Discrete Complex Systems, Lecture Notes in Computer Science Volume 9099, 2015, pp 113-126.
  37. Nazim Fatès, Biswanath Sethi, Sukanta Das, On the reversibility of ECAs with fully asynchronous updating: the recurrence point of view, Preprint, 2017.
  38. F. Fauvet, L. Foissy, D. Manchon, The Hopf algebra of finite topologies and mould composition, arXiv preprint arXiv:1503.03820, 2015
  39. Frederic Fauvet, L Foissy, D Manchon, Operads of finite posets, arXiv preprint arXiv:1604.08149, 2016
  40. Bernadette Faye, Florian Luca, Pieter Moree, On the discriminator of Lucas sequences, arXiv:1708.03563 [math.NT], 2017.
  41. YN Fedorov, ANW Hone, Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties, arXiv preprint arXiv:1512.00056, 2015
  42. J. M. Fedou, Enumeration of skew Ferrers diagrams and basic Bessel functions, Journal of Statistical Planning and Inference, Volume 34, Issue 1, January 1993, Pages 107-123.
  43. J.-M. Fedou, G. Fici, Some remarks on differentiable sequences and recursivity, JIS 13 (2010) #10.3.2
  44. Greg Fee, Simon Plouffe, An efficient algorithm for the computation of Bernoulli numbers (2007), arXiv:math/0702300
  45. Ad Feelders, Linda C. van der Gaag, Learning Bayesian network parameters under order constraints, International Journal of Approximate Reasoning, Volume 42, Issues 1-2, May 2006, Pages 37-53.
  46. J. Feigenbaum, A. D. Jaggard, M. Schapira, Approximate Privacy: Foundations and Quantification, ACM Transactions on Algorithms (TALG), Volume 10 Issue 3, June 2014. Article No. 11
  47. Feigin, Evgeny, Degenerate flag varieties and the median Genocchi numbers. Math. Res. Lett. 18 (2011), no. 6, 1163-1178.
  48. E. Feigin, The median Genocchi numbers, Q-analogues and continued fractions, Arxiv preprint arXiv:1111.0740, 2011
  49. Pedro Feijao, Reconstruction of ancestral gene orders using intermediate genomes, BMC Bioinformatics 2015, 16 (Suppl 14):S3; doi:10.1186/1471-2105-16-S14-S3; Proceedings of the 13th Annual Research in Computational Molecular Biology (RECOMB) Satellite Workshop on Comparative Genomics: Bioinformatics
  50. P. Feijao, F. V. Martinez, A Thevenin, On the Multichromosomal Hultman Number, Advances in Bioinformatics and Computational Biology, Lecture Notes in Computer Science Volume 8826, 2014, pp 9-16; Brazilian Symposium on Bioinformatics, BSB 2014, Belo Horizonte, Brazil, October 28-30, 2014, Proceedings; doi:10.1007/978-3-319-12418-6_2
  51. P Feijão, FV Martinez, A Thévenin, On the distribution of cycles and paths in multichromosomal breakpoint graphs and the expected value of rearrangement distance, BMC Bioinformatics, 2015, 16(Suppl. 19): S1; doi:10.1186/1471-2105-16-S19-S1
  52. T. Feil, K. Hutson, R. M. Kretchmar, Tree Traversals and permutations, Congr. Numer. 172 (2005) 201-221
  53. G. Feinberg, K.-H. Lee, Homogeneous representations of KLR-algebras and fully commutative elements, arXiv preprint arXiv:1401.0845, 2014
  54. Philip Feinsilver and John McSorley, Zeons, Permanents, the Johnson Scheme, and Generalized Derangements, International Journal of Combinatorics, Volume 2011, Article ID 539030, 29 pages; doi:10.1155/2011/539030.
  55. Andrew Feist, Fun with the (n) function.
  56. Leonid G. Fel, On Summatory Totient Functions (2008); arXiv:0802.0619
  57. D. P. Feldman and J. P. Crutchfield, Synchronizing to Periodicity: The Transient Information and Synchronization Time of Periodic Sequences, Santa Fe Institute Working Paper 02-08-043. arXiv:nlin/0208040. 2002.
  58. Stefan Felsner, \'Eric Fusy, Marc Noy et al., Bijections for Baxter Families and Related Objects (2008); arXiv:0803.1546
  59. Felsner, Stefan; Trotter, William T., Posets and planar graphs. J. Graph Theory 49 (2005), no. 4, 273-284.
  60. Guglielmo Feltrin. Positive subharmonic solutions to superlinear ODEs with indefinite weight. arXiv:1701.06145 [math.CA], 2017.
  61. D.-J. Feng, P. Liardet and A. Thomas, Partition functions in numeration systems with bounded multiplicity, Uniform Distribution Theory, submitted 2013,
  62. Jo Fenstad, Deciphering the hidden Pascal code of Guggenheim's quasichemical model. Overcoming computational limitations by use of Pascal's triangle, Journal of Mathematical Chemistry, Volume 42, Number 4 / November, 2007.
  63. V. Féray, Cyclic inclusion-exclusion, arXiv preprint arXiv:1410.1772, 2014
  64. R. Feria-Puron, H. Perez-Roses, J. Ryan, Searching for Large Circulant Graphs, arXiv preprint arXiv:1503.07357, 2015
  65. R. Feria-Purón, J. Ryan, H. Pérez-Rosés, Searching for Large Multi-Loop Networks, Electronic Notes in Discrete Mathematics, Volume 46, September 2014, Pages 233-240
  66. Emmanuel Ferrand, "Deformations of the Taylor Formula", J. Integer Sequences, Volume 10, 2007, Article 07.1.7.
  67. Luca Ferrari, Some combinatorics related to central binomial coefficients: Grand-Dyck paths, coloured noncrossing partitions and signed pattern avoiding permutations (2008); arXiv:0806.0973
  68. Luca Ferrari, Schroder partitions, Schroder tableaux and weak poset patterns, arXiv preprint arXiv:1606.06624, 2016
  69. Ferrari, L.; Grazzini, E.; Pergola, E.; Rinaldi, S. Some bijective results about the area of Schroeder paths. Random generation of combinatorial objects and bijective combinatorics. Theoret. Comput. Sci. 307 (2003), no. 2, 327-335.
  70. Luca Ferrari and Emanuele Munarini, Enumeration of saturated chains in Dyck lattices, Arxiv preprint arXiv:1203.6807, 2012
  71. Luca Ferrari and Emanuele Munarini, Enumeration of edges in some lattices of paths, Arxiv preprint arXiv:1203.6792, 2012
  72. L. Ferrari, E. Pergola, R. Pinzani and S. Rinaldi, Jumping succession rules and their generating functions, Discrete Math., 271 (2003), 29-50.
  73. Ferrari, Luca; Pergola, Elisa; Pinzani, Renzo; Rinaldi, Simone Some applications arising from the interactions between the theory of Catalan-like numbers and the ECO method. Ars Combin. 99 (2011), 109-128.
  74. L. Ferrari, E. Pergola, R. Pinzani, S. Rinaldi et al. An algebraic characterization of the set of succession rules, Selected papers in honour of Maurice Nivat. Theoret. Comput. Sci. 281 (2002), no. 1-2, 351-367.
  75. José William Porras Ferreira, An Approach to Solve Erdös-Straus Conjecture, ResearchGate, 2017.
  76. Luan Alberto Ferreira and Hugo Luiz Mariano, Some Consequences of the Firoozbakht's Conjecture, arXiv:1604.03496v2, 2017.
  77. R. Ferrer-i-Cancho, Non-crossing dependencies: least effort, not grammar, arXiv preprint arXiv:1411.2645, 2014
  78. L. Ferretti, F. Disanto and T. Wiehe, The Effect of Single Recombination Events on Coalescent Tree Height and Shape, PLoS ONE 8(4): e60123. doi:10.1371/journal.pone.0060123.
  79. J. Ferte, V. Pilaud and M. Pocchiola, On the number of simple arrangements of five double pseudolines. Discrete Comput. Geom. 45 (2011), 279-302.
  80. Laurent Feuilloley, Brief Announcement: Average Complexity for the LOCAL Model, preprint arXiv:1505.05072 [cs.DC], 2017. (A000788)
  81. Laurent Feuilloley, How Long It Takes for an Ordinary Node with an Ordinary ID to Output?, arXiv:1704.05739 [cs.DC], 2017.
  82. C. J. Fewster, D. Siemssen, Enumerating Permutations by their Run Structure, arXiv preprint arXiv:1403.1723, 2014
  83. Maximilian Fichtner, K Voigt, S Schuster, The tip and hidden part of the iceberg: Proteinogenic and non-proteinogenic aliphatic amino acids, Biochimica et Biophysica Acta (BBA)-General, 2016, Volume 1861, Issue 1, Part A, January 2017, Pages 3258-3269;
  84. Gabriele Fici, Open and Closed Words, in Giovanni Pighizzini, ed., The Formal Language Theory Column, Bulletin of EATCS, 2017,
  85. G. Fici and Zs. Liptak, doi:10.1007/978-3-642-22321-1_20 On Prefix Normal Words, Lecture Notes in Computer Science 6795 (2011) 228-238; also
  86. Gabriele Fici, Filippo Mignosi, Jeffrey Shallit, Abelian-square-rich words, Theoretical Computer Science, Volume 684, 2017, pp. 29-42. arXiv preprint arXiv:1701.00948
  87. Dan Fielder, Some thoughts on rook polynomials on square chessboards, in: Applications of Fibonacci Numbers, vol 9 (2004), Kluwer, p. 101-108
  88. James Allen Fill, Svante Janson and Mark Daniel Ward, Partitions with Distinct Multiplicities of Parts: On An "Unsolved Problem" Posed By Herbert Wilf, Arxiv preprint arXiv:1203.2670, 2012
  89. Peter E. Finch, From spin to anyon notation: The XXZ Heisenberg model as a D_3 (or su(2)_4) anyon chain, Arxiv preprint arXiv:1201.4470, 2012
  90. S. R. Finch, Mathematical Constants, Cambridge University Press (to appear), 2003. (Sample Essays and Supplementary Materials)
  91. Steven Finch, Pattern-Avoiding Permutations [There is a cached copy attached to A005802]
  92. S. R. Finch, Idempotents and Nilpotents Modulo n, arXiv:math.NT/0605019
  93. Steven Finch, Powers of Euler's q-Series, arXiv:math.NT/0701251.
  94. Steven Finch, Cilleruelo's LCM Constants,, 2013.
  95. S. Finch, <a href="">Toothpicks and live cells</a>
  96. S. Finch, Average least nonresidues
  97. Steven Finch and Pascal Sebah, Squares and Cubes Modulo n, arXiv:math.NT/0604465.
  98. S. Finch, P. Sebah and Z.-Q. Bai, Odd Entries in Pascal's Trinomial Triangle arXiv:0802.2654
  99. Alex Fink, Aviezri S. Fraenkel and Carlos Santos, LIM is not slim, International Journal of Game Theory, May 2013
  100. Thomas M. A. Fink, Emmanuel Barillot, and Sebastian E. Ahnert, Dynamics of network motifs, PDF, 2006.
  101. H. Finner and K. Strassburger, (2001). Increasing sample sizes do not always increase the power of UMPU-tests for 2x2-tables. Metrika, 54, 77-91.
  102. Lukas Finschi, A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids, A dissertation submitted to the Swiss Federal Institute of Technology, Zurich for the degree of Doctor of Mathematics, 2001.
  103. H. M. Finucan, Some decompositions of generalized Catalan numbers, pp. 275-293 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. Oates-Williams and A. P. Street. Lecture Notes Math., 952. Springer-Verlag, 1982.
  104. M. C. Firengiz, A. Dil, Generalized Euler–Seidel method for second order recurrence relations, Notes on Number Theory and Discrete Mathematics, Vol. 20, 2014, No. 4, 21–32; PDF
  105. F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1.
  106. Eldar Fischer, Tomer Kotek, and Johann A. Makowsky, Application of Logic to Combinatorial Sequences and Their Recurrence Relations,
  107. Johannes Fischer and Florian Kurpicz, Fast and Simple Parallel Wavelet Tree and Matrix Construction, arXiv:1702.07578 [cs.DS], 2017.
  108. Mareike Fischer, V Liebscher, On the Balance of Unrooted Trees, arXiv preprint arXiv:1510.07882, 2015
  109. P. M. Fishbane and P. Kaus, Neutrino Oscillations in Matter of Varying Density, J. Phys. G: Nucl. Part. Phys., 2001, v.27, N.12, p. 2405-14. arXiv:hep-ph/0101013
  110. Fishburn, Peter C.; Reeds, James A. Counting split semiorders. Order 18 (2001), no. 2, 119-128.
  111. Peter C. Fishburn, Fred S. Roberts, Elementary sequences, sub-Fibonacci sequences, Discrete Applied Mathematics, Volume 44, Issues 1-3, 19 July 1993, Pages 261-281.
  112. Susanna Fishel, Elizabeth Milićević, Rebecca Patrias, Bridget Eileen Tenner, Enumerations relating braid and commutation classes, arXiv:1708.04372 [math.CO], 2017.
  113. M. J. Fisher et al., The birank number of a graph, Congressus Numerant., 204 (2010), 173-180.
  114. T. A. Fisher, A Caldero-Chapoton map depending on a torsion class, arXiv preprint arXiv:1510.07484, 2015
  115. Francesc Fite, Kiran S. Kedlaya, Victor Rotger and Andrew V. Sutherland, Sato-Tate distributions and Galois endomorphism modules in genus 2, Arxiv preprint arXiv:1110.6638, 2011
  116. Francesc Fite and Andrew V. Sutherland, Sato-Tate distributions of twists of y^2= x^5-x and y^2= x^6+1, Arxiv preprint arXiv:1203.1476, 2012.
  117. P. Flajolet, A Problem in Statistical Classification Theory, Studies in Automatic Combinatorics, Volume I (1996).
  118. P. Flajolet, Enumerating alcohols and other classes of chemical molecules, an example of Polya's theory , Studies in Automatic Combinatorics, Volume I (1996).
  119. P. Flajolet, Balls and Urns, Etc., Studies in Automatic Combinatorics, Volume I (1996).
  120. Philippe Flajolet, Eric Fusy, Xavier Gourdon, Daniel Panario and Nicolas Pouyanne, arXiv:math.CO/0606370 A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics, Electron. J. Combin. 13 (2006), no. 1, Research Paper 103, 35 pp.
  121. Flajolet, Philippe; Gerhold, Stefan; Salvy, Bruno, On the non-holonomic character of logarithms, powers and the nth prime function. Electron. J. Combin. 11 (2004/06), no. 2, Article 2, 16 pp.
  122. P. Flajolet, K. Hatzis, S. Nikoletseas and P. Spirakis, On the Robustness of Interconnections in Random Graphs: A Symbolic Approach, Algorithms (Prague, 1999). Theoret. Comput. Sci. 287 (2002), no. 2, 515-534.
  123. P. Flajolet and M. Noy, Analytic Combinatorics of Noncrossing Configurations, Discrete Math. 204 (1999), 203-229 (Selected papers in honor of Henry W. Gould). The version available here is a preliminary version: INRIA RR3196, June 1997, 22 pages [ ps]. (Only the printed version mentions the On-Line Encyclopedia of Integer Sequences.)
  124. P. Flajolet, P. Poblete and A. Viola, On the Analysis of Linear Probing Hashing, (INRIA, RR3265), September 1997. 22 pages. In Algorithmica 22, (December 1998), pp. 490-515. (Special Issue on Analysis of Algorithms.)
  125. Philippe Flajolet, Helmut Prodinger, Level number sequences for trees, Discrete Mathematics, Volume 65, Issue 2, June 1987, Pages 149-156.
  126. P. Flajolet and B. Salvy, Computer algebra libraries for combinatorial structures. Journal of Symbolic Computation, vol. 20, no. 5-6, 1995, pages 653-671.
  127. P. Flajolet, B. Salvy and P. Zimmermann, Automatic average-case analysis of algorithms. Theoretical Computer Science, Series A, vol. 79, no. 1, February 1991, pages 37-109.
  128. P. Flajolet and R. Sedgewick, Analytic Combinatorics--Symbolic Combinatorics, 186p.+viii, May 2002.
  129. P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge University Press, 810p.+xiv, January 2009.[1]
  130. S. D. Flaten, Energy Efficient Reed-Solomon Error Correction, Master of Science in Electronics Dissertation, Norwegian University of Science and Technology, Trondheim, 2013;
  131. Daniel Flath, Tom Halverson, Kathryn Herbig, The planar rook algebra and Pascal's triangle, arXiv:0806.3960 [math.RT]
  132. Anthony Flatters, doi:10.1016/j.jnt.2008.05.008 Primitive Divisors of some Lehmer-Pierce Sequences] (2007), arXiv:0708.2190; Journal of Number Theory, Volume 129, Issue 1, January 2009, Pages 209-219.
  133. Anthony Flatters, Power Values of Certain Quadratic Polynomials (2009) arXiv:0901.3461
  134. A. Flaxman, A. W. Harrow and G. B. Sorkin, Strings with maximally many distinct subsequences and substrings (Citeseer), Electron. J. Combin. 11 (2004), no. 1, Research Paper 8, 10 pp.
  135. Martin Fleck, Javier Troya, Marouane Kessentini, Manuel Wimmer and Bader Alkhazi, Model Transformation Modularization as a Many-Objective Optimization Problem, IEEE Transactions on Software Engineering, (Volume: PP, Issue: 99) 2017. doi:10.1109/TSE.2017.2654255
  136. Pierre Flener, Justin Pearson, Solving necklace constraint problems, Journal of Algorithms, Volume 64, Issues 2-3, April-July 2009, Pages 61-73.
  137. Felix Flicker, Time Quasicrystals in Dissipative Dynamical Systems, arXiv:1707.09371 [nlin.CD], 2017.
  138. Peter Floodstrand Blanchard, Pseudo-arithmetic sets and Ramsey theory, Journal of Combinatorial Theory, Series A, Volume 106, Issue 1, April 2004, Pages 49-57.
  139. Laura Florescu, Daniela Morar, David Perkinson, Nicholas Salter, Tianyuan Xu, Sandpiles and Dominos, Electronic Journal of Combinatorics, Volume 22(1), 2015. ["We would like to acknowledge the mathematical software Sage [44] and the Online Encyclopedia of Integer Sequences [33] which were both essential for our investigations."]
  140. R. Flórez, R. A. Higuita, A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014).
  141. Rigoberto Flórez, Robinson A. Higuita, Antara Mukherjee, Star of David and other patterns in the Hosoya-like polynomials triangles, arXiv:1706.04247 [math.CO], 2017.
  142. Jean-Pierre Flori, Fonctions booleennes, courbes algebriques et multiplication complexe, Thesis, ParisTech, Feb 03 2012;
  143. Timothy B. Flowers, Extending a Recent Result on Hyper m-ary Partition Sequences, Journal of Integer Sequences, Vol. 20 (2017), #17.6.7.
  144. Dominique Foata and Guo-Niu Han, Dimers and new q-tangent numbers, Preprint, Oct. 2008.
  145. Dominique Foata and Guo-Niu Han, The dimer polynomial triangle, Preprint, Oct. 2008.
  146. D. Foata and G.-N. Han, doi:10.1007/s11139-009-9194-9 The doubloon polynomial triangle, Ramanujan J. 23 (2010) 107-126
  147. Dominique Foata and Guo-Niu Han, Multivariable Tangent and Secant q-derivative Polynomials, arXiv:1304.2486
  148. Foata, Dominique and Han, Guo-Niu, Doubloons and new Q-tangent numbers. Q. J. Math. 62 (2011), no. 2, 417-432.
  149. D. Foata and G.-N. Han, Tree Calculus for Bivariable Difference Equations, 2012,
  150. D. Foata and G.-N. Han, Secant Tree Calculus, arXiv preprint arXiv:1304.2485, 2013
  151. Dominique Foata and Guo-Niu Han, Seidel Triangle Sequences and Bi-Entringer Numbers, November 20, 2013;
  152. D Foata, GN Han, Andre Permutation Calculus; a Twin Seidel Matrix Sequence, arXiv preprint arXiv:1601.04371, 2016
  153. D. Foata, G.-N. Han and B. Lass, Les nombres hyperharmoniques et la fratrie du collectionneur de vignettes, Sémin. Lothar. Comb. 47, B47a, 20 p., electronic only (2001).
  154. Foata, D. and Krattenthaler, C., Graphical Major Indices, II, Seminaire Lotharingien de Combinatoire, B34k, 16 pp., 1995.
  155. D. Foata and D. Zeilberger, The graphical major index, J. Comput. Applied Math (special issue on q-series) 68 (1996) 79-101.
  156. D. Foata and D. Zeilberger, A classic proof of a recurrence for a very classical sequence, J. Combin. Theory Ser. A 80 (1997), no. 2, 380-384. (Note: the on-line version of this paper does not mention the Encyclopedia)
  157. Foissy, L., Finite-dimensional comodules over the Hopf algebra of rooted trees. J. Algebra 255 (2002), no. 1, 89-120.
  158. Foissy, L., Free and cofree Hopf algebras. J. Pure Appl. Algebra 216 (2012), no. 2, 480-494.
  159. Loïc Foissy, Ordered forests and parking functions. Int. Math. Res. Not. IMRN 2012, no. 7, 1603-1633.
  160. Loïc Foissy, The Hopf algebra of Fliess operators and its dual pre-Lie algebra, 2013;
  161. Loïc Foissy, Free quadri-algebras and dual quadri-algebras, preprint arXiv:1504.06056 (A007297, A085614, A078531)
  162. L. Foissy and C. Malvenuto, The Hopf algebra of finite topologies and T-partitions, arXiv preprint arXiv:1407.0476, 2014
  163. L. Foissy, C. Malvenuto, F. Patras, B_infinity-algebras, their enveloping algebras, and finite spaces, arXiv preprint arXiv:1403.7488, 2014
  164. Loic Foissy, Claudia Malvenuto, Frederic Patras, Infinitesimal and B_infinity-algebras, finite spaces, and quasi-symmetric functions, Journal of Pure and Applied Algebra, Elsevier, 2016, 220 (6), pp. 2434-2458. <hal-00967351v2>.
  165. L. Foissy and F. Patras, Natural endomorphisms of shuffle algebras, Arxiv preprint arXiv:1205.2986, 2012
  166. Amanda Folsom, S Garthwaite, SY Kang, H Swisher et al., Quantum mock modular forms arising from eta-theta functions, arXiv preprint arXiv:1604.00941, 2016
  167. A. Folsom, K. Ono and R. C. Rhoades, Ramanujan's radial limits,, 2013.
  168. Sergey Fomin and Grigory Mikhalkin, Labeled floor diagrams for plane curves, arXiv:0906.3828. J. Eur. Math. Soc. (JEMS) 12 (2010), no. 6, 1453–1496.
  169. Fomin, Sergey; Reading, Nathan, Generalized cluster complexes and Coxeter combinatorics. Int. Math. Res. Not. 2005, no. 44, 2709-2757.
  170. T. Fonseca, F. Balogh, The higher spin generalization of the 6-vertex model with domain wall boundary conditions and Macdonald polynomials, Journal of Algebraic Combinatorics, 2014; doi:10.1007/s10801-014-0555-0
  171. Felix Fontein and Pawel Wocjan, Quantum Algorithm for Computing the Period Lattice of an Infrastructure, Arxiv preprint arXiv:1111.1348, 2011
  172. F. Fontein and P. Wocjan, On the Probability of Generating a Lattice, arXiv preprint arXiv:1211.6246, 2012
  173. Stefan Forcey, Convex Hull Realizations of the Multiplihedra (2007), arXiv:0706.3226; Topology and its Applications, Volume 156, Issue 2, 1 December 2008, Pages 326-347.
  174. S. Forcey, M. Kafashan, M. Maleki and M. Strayer, Recursive bijections for Catalan objects, arXiv preprint arXiv:1212.1188, 2012
  175. Stefan Forcey, Aaron Lauve, Frank Sottile, New Hopf Structures on Binary Trees, dmtcs:2740 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
  176. Stefan Forcey, Aaron Lauve, Frank Sottle, Cofree compositions of coalgebras (extended abstract), arXiv:1011.4305 [math.CO]
  177. Stefan Forcey, Aaron Lauve, Frank Sottle, Cofree compositions of coalgebras, arXiv:1012.3483; Annals of Combinatorics 17 (1) pp.105-130 March, 2013;
  178. Forcey, Stefan; Lauve, Aaron; and Sottile, Frank; Hopf structures on the multiplihedra. SIAM J. Discrete Math. 24 (2010), no. 4, 1250-1271.
  179. Stefan Forcey, M Ronco, P Showers, Polytopes and algebras of grafted trees: Stellohedra, arXiv preprint arXiv:1608.08546, 2016
  180. Kevin Ford, Florian Luca and Pieter Moree, Values of the Euler phi-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields, Arxiv preprint arXiv:1108.3805, 2011
  181. A. P. Fordy, Periodic Cluster Mutations and Related Integrable Maps, arXiv preprint arXiv:1403.8061, 2014
  182. A. Fordy and A. Hone, Discrete integrable systems and Poisson algebras from cluster maps, Arxiv preprint arXiv:1207.6072, 2012
  183. Allan P. Fordy and Robert J. Marsh, Cluster mutation-periodic quivers and associated Laurent sequences, arXiv:0904.0200; J. Algebraic Combin. 34 (2011), no. 1, 19-66.
  184. Foreman, Erika D., "Order automorphisms on the lattice of residuated maps of some special nondistributive lattices." (2015). Univ. Louisville, Electronic Theses and Dissertations. Paper 2257. doi:10.18297/etd/2257;
  185. Roman Forker, Matthias Meissner, and Torsten Fritz, Classification of epitaxy in reciprocal and real space: rigid versus flexible lattices, Soft Matter, 13(9), 2017, pp. 1748-1758. doi:10.1039/c6sm02688e
  186. P. J. Forrester, A. Mays, Finite size corrections in random matrix theory and Odlyzko's data set for the Riemann zeros, arXiv preprint arXiv:1506.06531, 2015
  187. Richard Fors, Independence Complexes of Certain Families of Graphs, Master thesis in Mathematics at KTH, Presented August 19, 2011;
  188. L. Forsberg, Effective representations of Hecke-Kiselman monoids of type A, Arxiv preprint arXiv:1205.0676, 2012
  189. M. Forsyth, A. Jayakumar, J. Shallit, Remarks on Privileged Words, arXiv preprint arXiv:1311.7403, 2013
  190. J. Fortier, A. Goupil, J. Lortie and J. Tremblay, Exhaustive generation of gominoes, Theoretical Computer Science, 2012; doi:10.1016/j.tcs.2012.02.032
  191. D. Fortin, B-SPLINE TOEPLITZ INVERSE UNDER CORNER PERTURBATIONS, International Journal of Pure and Applied Mathematics, Volume 77, No. 1, 2012, 107-118;
  192. P. Fortuny Ayuso, J. M. Grau, A. Oller-Marcen, A von Staudt-type formula for sum(z in Z_n[i]) z^k, arXiv:1402.0333
  193. P. Fortuny, J.M. Grau, A.M. Oller-Marcén, I.F. Rúa, arXiv:1505.08132 On power sums of matrices over a finite commutative ring, arXiv preprint, 2015. (A017593)
  194. Colin Foster, Peripheral mathematical knowledge, For the Learning of Mathematics, vol. 31, #3 (November, 2011), pp. 24-28; PDF.
  195. B. Foster-Greenwood, C. Kriloff, Spectra of Cayley Graphs of Complex Reflection Groups, arXiv preprint arXiv:1502.07392, 2015
  196. F. Foucaud, R. Klasing, P.J. Slater, Centroidal bases in graphs, arXiv preprint arXiv:1406.7490, 2014
  197. Nathan Fox, On Aperiodic Subtraction Games with Bounded Nim Sequence, arXiv preprint arXiv:1407.2823, 2014
  198. Nathan Fox, Finding Linear-Recurrent Solutions to Hofstadter-Like Recurrences Using Symbolic Computation, arXiv:1609.06342, 2016.
  199. Nathan Fox, A Slow Relative of Hofstadter's Q-Sequence, arXiv preprint arXiv:1611.08244, 2016
  200. Norman B. Fox, Combinatorial Potpourri: Permutations, Products, Posets, and Pfaffians, University of Kentucky, Theses and Dissertations, Mathematics, Paper 25. (A081091)
  201. Fraenkel, Aviezri S. "Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups." Transactions of the American Mathematical Society 341.2 (1994): 639-664.
  202. A. S. Fraenkel, arXiv:math.CO/9809074 Heap games, numeration systems and sequences, Annals of Combinatorics, 2 (1998) 197-210.
  203. A. S. Fraenkel, Arrays, numeration systems and Frankenstein games, FUN with algorithms (Elba, 1998). Theoret. Comput. Sci. 282 (2002), no. 2, 271-284.
  204. A. S. Fraenkel, Mathematical Chats Between Two Physicists, in Puzzlers' Tribute: A Feast for the Mind, honoring Martin Gardner (D. Wolfe and T. Rodgers, eds.), A. K. Peters, 2002, pp. 315-325.
  205. A. S. Fraenkel, New games related to old and new sequences, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.
  206. A. S. Fraenkel, From enmity to amity, Amer. Math. Monthly, 117 (2010) , 646-648. [The Abstract begins "Sloane's influential On-Line Encyclopedia of Integer Sequences is an indispensable research tool in the service of the mathematical community..."]
  207. Aviezri S. Fraenkel, The vile, dopy, evil and odious game players, Discrete Math., 312 (2011), 42-46.
  208. Aviezri S. Fraenkel, Aperiodic subtraction games, El. J. Combin. 18 (2) (2011) #P19
  209. A. S. Fraenkel, Ratwyt, 2011; Also The College Mathematics Journal, Vol. 43, No. 2 (March 2012), pp. 160-164.
  210. Aviezri S. Fraenkel and Urban Larsson, Playability and arbitrarily large rat games, arXiv:1705.03061 [math.CO], 2017.
  211. Nevena Francetić, Sarada Herke, Ian M. Wanless, Parity of Sets of Mutually Orthogonal Latin Squares, arXiv:1703.04764 [math.CO], 2017.
  212. Francisco, Christopher A.; Mermin, Jeffrey; Schweig, Jay; Borel generators. J. Algebra 332 (2011), 522-542.
  213. C. A. Francisco, J. Mermin, J. Schweig, Catalan numbers, binary trees, and pointed pseudotriangulations, 2013;
  214. F. Franek, S. Gao, W. Lu, P. J. Ryan, W. F. Smyth, Yu Sun and L. Yang, Verifying a border array in linear time, J. Combinatorial Math. and Combinatorial Computing 42 (2002) to appear.
  215. Ghislain R. Franssens, "On a Number Pyramid Related to the Binomial, Deleham, Eulerian, MacMahon and Stirling number triangles", J. Integer Sequences, Volume 9, 2006, Article 06.4.1.
  216. Z. Franusic, On the Extension of the Diophantine Pair {1,3} in Z[surd d], J. Int. Seq. 13 (2010) # 10.9.6
  217. H Franzen, T Weist, The Value of the Kac Polynomial at One, arXiv preprint arXiv:1608.03419, 2016
  218. Fabrizio Frati, M Patrignani, V Roselli, LR-Drawings of Ordered Rooted Binary Trees and Near-Linear Area Drawings of Outerplanar Graphs, arXiv preprint arXiv:1610.02841, 2016
  219. J. Freeman, MetaMix: Between Unity and Collaboration.
  220. W. Freeman, A method for the compact and efficient encoding of ordinal primes, YCS technical report, 2003.
  221. D. Freittloh, Highly symmetric fundamental cells for lattices in R^2 and R^3, arXiv:1305.1798, 2013.
  222. J. Freixas and S. Kurz, The golden number and Fibonacci sequences in the design of voting structures, PDF, 2012.
  223. Darrin D. Frey and James A. Sellers, "Jacobsthal Numbers and Alternating Sign Matrices", J. Integer Sequences, Volume 3, 2000, Article 00.2.3.
  224. Darrin D. Frey and James A. Sellers, "On Powers of 2 Dividing the Values of Certain Plane Partition Functions", J. Integer Sequences, Volume 4, 2001, Article 01.1.8.
  225. Peter J. Freyd, Core algebra revisited, Theoretical Computer Science, 375 (2007), Issues 1-3, 193-200.
  226. Erich Friedman and Mike Keith, "Magic Carpets", J. Integer Sequences, Volume 3, 2000, Article 00.2.5.
  227. Tamar Friedmann, JR Harper, On H-Spaces and a Congruence of Catalan Numbers, arXiv preprint arXiv:1612.03837, 2016
  228. Fritzsche, Bernd; Kirstein, Bernd; Mädler, Conrad On Hankel nonnegative definite sequences, the canonical Hankel parametrization, and orthogonal matrix polynomials. Complex Anal. Oper. Theory 5 (2011), no. 2, 447-511
  229. B. Fritzsche, B. Kirstein and C. Madler, On a Schur-type Algorithm for Sequences of Complex p×q-matrices and its Interrelations with the Canonical Hankel Parametrization, pp. 117-192 in Interpolation, Schur Functions and Moment Problems II, Daniel Alpay, Bernd Kirstein (eds.), Operator Theory: Advances and Applications, Vol. 226, 211-250, 2112, Birkhauser Basel.
  230. B. Fritzsche, B. Kirstein and C. Madler, On a Special Parametrization of Matricial alpha-Stieltjes One-sided Non-negative Definite Sequences, in Interpolation, Schur Functions and Moment Problems II, Daniel Alpay, Bernd Kirstein (eds.), Operator Theory: Advances and Applications, Vol. 226, 211-250, 2112, Birkhauser Basel.
  231. J. Fromentin, Exploring the tree of numerical semigroups, 2013,
  232. A. Frosini and S. Rinaldi, "On the Sequence A079500 and Its Combinatorial Interpretations", J. Integer Sequences, Volume 9, 2006, Article 06.3.1.
  233. Christiane Frougny, Edita Pelantová, and Milena Svobodová, "Minimal Digit Sets for Parallel Addition in Non-Standard Numeration Systems", Journal of Integer Sequences, Vol. 16 (2013), #13.2.17.
  234. Timothy J Frye, Recursive Relationships in the Classes of Odd Graphs and Middle Levels Graphs, arXiv preprint arXiv:1611.06401, 2016
  235. Hao Fu, GN Han, Computer assisted proof for Apwenian sequences related to Hankel determinants, arXiv preprint arXiv:1601.04370, 2016
  236. H.-L. Fu, Y.-H. Lo and K. W. Shum, Optimal conflict-avoiding codes of odd length and weight three, Designs, Codes and Cryptography, Nov. 2012; doi:10.1007/s10623-012-9764-5.
  237. Shishuo Fu, Z. Lin, J. Zeng, Two new unimodal descent polynomials, arXiv preprint arXiv:1507.05184, 2015
  238. Shishuo Fu and James Sellers, Enumeration of the degree sequences of line-Hamiltonian multigraphs, INTEGERS 12 (2012), #A24.
  239. Shishuo Fu, D Tang, Partitions with fixed largest hook length, arXiv preprint arXiv:1604.04028, 2016
  240. Shishuo Fu, Dazhao Tang, Generalizing a partition theorem of Andrews, arXiv:1705.05046, 2017 [math.CO]
  241. Y. Fujiwara, Parsing a Sequence of Qubits, IEEE Trans. Information Theory, 59 (2013), 6796-6806.
  242. H. Fuks, Adam Adamandy Kochanski's approximations of pi: reconstruction of the algorithm, Arxiv preprint arXiv:1111.1739, 2011. Also The Mathematical Intelligencer, December 2012, Volume 34, Issue 4, pp. 40-45.
  243. H. Fuks and J. M. G. Soto, Exponential convergence to equilibrium in cellular automata asymptotically emulating identity, arXiv preprint arXiv:1306.1189, 2013
  244. Motohisa Fukuda, Ion Nechita, Enumerating meandric systems with large number of components, arXiv preprint arXiv:1609.02756, 2016
  245. Neale L. Fulton, Mark Westcott, Warren F. Smith, Constructing a Feasible Design Space for Multiple Cluster Conflict and Taskload Assessment, In: Sarker R., Abbass H., Dunstall S., Kilby P., Davis R., Young L. (eds) Data and Decision Sciences in Action, Lecture Notes in Management and Industrial Engineering. doi:10.1007/978-3-319-55914-8_15
  246. Fusy, Éric, Counting d-polytopes with d+3 vertices. Electron. J. Combin. 13 (2006), no. 1, Research Paper 23, 25 pp.

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.


  1. A concordance between OEIS and AC.
Retrieved from ""
Personal tools