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"When Erdenberger [6] appeared on the arXiv, John McKay immediately pointed out that this is the list of supersingular primes A002267, the primes that divide the order of the Monster..." [G. K. Sankaran, 2020]

"We used the Online Encyclopedia of Integer Sequences to trace related research..." [Luigi Santocanale, 2019]

"It was a knock-out when after entering the sequence 2,5,15,51,187,715,... in the page OEIS, we found a great variety of different interpretations for it..." [Carlos Segovia, 2013]

"The numbers that came out were 4, 28, 232, 2092, 19864, . . . and we couldn't see a pattern. In desperation, we sent them to (now (a miracle program created by Neil Sloane). ..." [SIAM News, 1999]

"The authors are thankful to the On-Line Encyclopedia of Integer Sequences [12], which drew their attention to plane permutations." [Jannik Silvanus and Jens Vygen, 2017]

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  • 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 Sa to Sk.
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  1. Ahmad Sabri and Vincent Vajnovszki, More restricted growth functions: Gray codes and exhaustive generations, arXiv:1703.05856 [math.CO], 2017.
  2. Ahmad Sabri, Vincent Vajnovszki, Exhaustive generation for ballot sequences in lexicographic and Gray code order, 2018. PDF (A000085)
  3. Ahmad Sabri, Vincent Vajnovszki, On the exhaustive generation of generalized ballot sequences in lexicographic and Gray code order, Pure Mathematics and Applications (2019) Vol. 28, Issue 1, 109-119. doi:10.1515/puma-2015-0035 (A000085)
  4. R. Sachdeva and A.K. Agarwal, Combinatorics of certain restricted n-color composition functions, Discrete Mathematics, 340, (2017), 361-372.
  5. J. Sack and H. Ulfarsson, Refined inversion statistics on permutations, Arxiv preprint arXiv:1106.1995, 2011.
  6. Yaniv Sadeh, Ori Rottenstreich, Arye Barkan, Yossi Kanizo, Haim Kaplan, Optimal Representations of a Traffic Distribution in Switch Memories, IEEE INFOCOM 2019 - IEEE Conference on Computer Communications. doi:10.1109/INFOCOM.2019.8737645
  7. Markus Saers, Dekai Wu and Chris Quirk, On the Expressivity of Linear Transductions, PDF.
  8. Pablo Saez, X. Vidaux, M. Vsemirnov, Optimal bounds for Buchi's problem in modular arithmetic, Journal of Number Theory Volume 149, April 2015, Pages 368-403.
  9. Bruce E. Sagan, Congruences via abelian groups, Journal of Number Theory, Volume 20, Issue 2, April 1985, Pages 210-237.
  10. Bruce Sagan, Proper partitions of a polygon and k-Catalan numbers (2004), arXiv:math/0407280 and Ars. Comb. 88 (2008) 109-124.
  11. Sage, Common Graphs (Graph Generators)
  12. Barun Kumar Saha, Sudip Misra, Sujata Pal, SeeR: Simulated Annealing-Based Routing in Opportunistic Mobile Networks, IEEE Transactions on Mobile Computing, Vol. 16, No. 10, October 2017. doi:10.1109/TMC.2017.2673842
  13. Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.
  14. Hanno Sahlmann, Entropy calculation for a toy black hole (2007), arXiv:0709.0076.
  15. Soumyadip Sahu, On Certain Reciprocal Sums, arXiv:1807.05454 [math.NT], 2018. (A248230, A248234)
  16. M. K. Sahukar and G. K. Panda, Repdigits in Euler functions of Pell numbers, Fib. Q., 57 (No. 2, 2019), 134-138.
  17. Monjul Saikia, Md. Anwar Hussain, "Location-Independent Key Distribution for Sensor Network Using Regular Graph", Progress in Computing, Analytics and Networking, Proceedings of ICCAN 2017 (2018), 1-8. doi:10.1007/978-981-10-7871-2
  18. R. Sainudiin, Algebra and Arithmetic of Plane Binary Trees, Slides of a talk, 2014;
  19. Raazesh Sainudiin, Statistical Regular Pavings in Bayesian Nonparametric Density Estimation, 2014;
  20. R. Sainudiin, Some Arithmetic, Algebraic and Combinatorial Aspects of Plane Binary Trees, Slides from a talk, Oct 27 2014;
  21. R Sainudiin, A Veber, A Beta-splitting model for evolutionary trees, arXiv preprint arXiv:1511.08828, 2015
  22. S. Saito, T. Tanaka, N. Wakabayashi, Combinatorial Remarks on the Cyclic Sum Formula for Multiple Zeta Values, J. Int. Seq. 14 (2011) # 11.2.4
  23. A. Sakhnovich, L. Sakhnovich, Nonlinear Fokker-Planck equation: stability, distance and corresponding extremal problem in the spatially inhomogeneous case, arXiv preprint arXiv:1307.1126, 2013
  24. Ana Salagean, David Gardner and Raphael Phan, Index Tables of Finite Fields and Modular Golomb Rulers, in Sequences and Their Applications - SETA 2012, Lecture Notes in Computer Science. Volume 7280, 2012, pp. 136-147.
  25. Sajad Salami, On special matrices related to Cauchy and Toeplitz matrices, Instítuto da Matemática e Estatística, Universidade Estadual do Rio de Janeiro (Brazil, 2019). PDF (A005249)
  26. J. Salas and A. D. Sokal, arXiv:cond-mat/0004330 Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models I. General Theory and Square-Lattice Chromatic Polynomial], J. Statist. Phys. 104 (2001) 609-699.
  27. J. Salas and A. D. Sokal, Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial, J. Stat. Phys. 135 (2009) 279-373, arXiv:0711.1738
  28. H Salehian, R Chakraborty, E Ofori, D Vaillancourt, An efficient recursive estimator of the Fréchet mean on a hypersphere with applications to Medical Image Analysis, Preprint 2015;
  29. A Salerno, D Schindler, A Tucker, Symmetries of Rational Functions Arising in Ecalle's Study of Multiple Zeta Values;, 2015; In: Women in Numbers Europe: Research Directions, Springer, 2015
  30. Ville Salo, Decidability and Universality of Quasiminimal Subshifts, arXiv preprint arXiv:1411.6644, 2014.
  31. Ville Salo, Universal gates with wires in a row, arXiv:1809.08050 [math.GR], 2018. (A000031)
  32. Ville Salo, Subshifts with sparse traces, University of Turki, Finland (2019). PDF (A055979)
  33. Ville Salo, Cutting Corners, arXiv:2002.08730 [math.DS], 2020. (A295928)
  34. D. Salomon, Variable-length Codes for Data Compression, Springer-Verlag.
  35. D. Salomon, G. Motta, doi:10.1007/978-1-84882-903-9, Handbook of data compression, Springer, 2010.
  36. V. Salov, Inevitable Dottie Number. Iterals of cosine and sine, arXiv:1212.1027, 2012
  37. E. Salturk and I. Siap, Generalized Gaussian Numbers Related to Linear Codes over Galois Rings, European Journal of Pure and Applied Mathematics, Vol. 5, No. 2, 2012, 250-259; ISSN 1307-5543;
  38. Paolo Salvatore and Roberto Tauraso, The operad Lie is free (2008); arXiv:0802.3010; Journal of Pure and Applied Algebra, Volume 213, Issue 2, February 2009, Pages 224-230.
  39. Rafaele Salvia, A catalogue of matchstick graphs, arXiv:1303.5965
  40. Ivano Salvo, Agnese Pacifico, Computing Integer Sequences: Filtering vs Generation (Functional Pearl), arXiv:1807.11792 [cs.PL], 2018. (A002858, A033629)
  41. B. Salvy, Automatic Asymptotics and Generating Functions, Algorithms seminar, 1992-1993, INRIA Research Report #2130, 47-50. (Ps, Pdf)
  42. B. Salvy, Découverte de récurrences
  43. B. Salvy and S. Yu. Slavyanov, A Combinatorial Problem in the Classification of Second-Order Linear ODE's, Research Report no. 2600, Institut National de Recherche en Informatique et en Automatique, 1995. 7 pages.
  44. B. Salvy and P. Zimmermann, Gfun: a Maple package for the manipulation of generating and holonomic functions in one variable. ACM Transactions on Mathematical Software, vol. 20, no. 2, 1994, pages 163-177.
  45. B. Sambale, Pseudo-Sylow numbers, Amer. Math. Monthly 126 (2019), 60-65.
  46. Benjamin Sambale, On a theorem of Ledermann and Neumann, arXiv:1909.13220 [math.GR], 2019. (A137315)
  47. Samieinia, Shiva, The number of Khalimsky-continuous functions on intervals. Rocky Mountain J. Math. 40 (2010), no. 5, 1667-1687.
  48. S. Samieinia, doi:10.4171/PM/1858, The number of continuous curves in digital geometry, Port. Mathem. 67 (1) (2010) 75-89
  49. M. J. Samuel, Word posets, with applications to Coxeter groups, Arxiv preprint arXiv:1108.3638, 2011.
  50. Pablo San Segundo, Fabio Furini, Jorge Artieda, A new branch-and-bound algorithm for the Maximum Weighted Clique Problem, Computers & Operations Research (2019) Vol. 110, 18-33. doi:10.1016/j.cor.2019.05.017 (A265032)
  51. F. M. Sanchez, Remarkable Properties of the Eddington Number 137 and Electric Parameter 137.036 excluding the Multiverse Hypothesis, 2015;
  52. Selene Sanchez-Flores, The Lie module structure on the Hochschild cohomology groups of monomial algebras with radical square zero (2007), arXiv:0711.2810; Journal of Algebra, Volume 320, Issue 12, 15 December 2008, Pages 4249-4269.
  53. J. Sander, J. Steuding, R. Steuding, Diophantine aspects of the Calkin-Wilf iteration, El. Math. 66 (2) (2011) 45-55 doi:10.4171/EM/170
  54. Maya Sankar, Further Bijections to Pattern-Avoiding Valid Hook Configurations, arXiv:1910.08895 [math.CO], 2019. (A005700, A005789, A151347)
  55. G. K. Sankaran, Locally symmetric varieties and holomorphic symplectic manifolds, University of Bath (UK, 2020). PDF (A002267)

When [6] appeared on the arXiv, John McKay immediately pointed out that this is the list of supersingular primes A002267, the primes that divide the order of the Monster: the same list, recognised by the same person, led to the Moonshine conjectures and the famous work of Borcherds (yielding, among many other things, the Borcherds form Φ). We still do not have a completely satisfactory explanation for this coincidence, although it is not completely mysterious. It is quite likely that it is an artefact of the proof: it could perfectly well be that, for example, A71 is in fact of general type.

  1. David Sankoff and Lani Haque, Power Boosts for Cluster Tests, in Comparative Genomics, Lecture Notes in Computer Science, Volume 3678/2005, Springer-Verlag.
  2. C. Sanna, On Arithmetic Progressions of Integers with a Distinct Sum of Digits, Journal of Integer Sequences, Vol. 15 (2012), #12.8.1.
  3. Carlo Sanna, On the number of distinct exponents in the prime factorization of an integer, arXiv:1902.09224 [math.NT], 2019. (A071625, A130091)
  4. Noriaki Sannomiya, H Katsura, Y Nakayama, Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion, arXiv preprint arXiv:1612.02285, 2016
  5. Joseph M. Santmyer, A stirling like sequence of rational numbers, Discrete Mathematics, Volume 171, Issues 1-3, 20 June 1997, Pages 229-235.
  6. Luigi Santocanale, On discrete idempotent paths, arXiv:1906.05590 [math.LO], 2019. (A001519, A001906, A088305, A144224) We used the Online Encyclopedia of Integer Sequences to trace related research...
  7. Santocanale, Luigi; Wehrung, Friedrich The extended permutohedron on a transitive binary relation. European J. Combin. 42 (2014), 179-206.
  8. L Santocanale, F Wehrung, G Grätzer, F Wehrung, Generalizations of the Permutohedron, in Grätzer G., Wehrung F. (eds) Lattice Theory: Special Topics and Applications. Birkhäuser, Cham, pp. 287-397; doi:10.1007/978-3-319-44236-5_8
  9. Andrés Santos, Density Expansion of the Equation of State, in A Concise Course on the Theory of Classical Liquids, Volume 923 of the series Lecture Notes in Physics, pp 33-96, 2016. doi:10.1007/978-3-319-29668-5_3
  10. F. Santos, C. Stump, V. Welker, Noncrossing sets and a Grassmann associahedron, arXiv preprint arXiv:1403.8133, 2014; also in FPSAC 2014, Chicago, USA; Discrete Mathematics and Theoretical Computer Science (DMTCS) Proceedings, 2014, 609-620.
  11. Biswajit Sanyal, S Majumder, WK Hon, Efficient Generation of Top-k Procurements in a Multi-item Auction, in WALCOM: Algorithms and Computation: 10th International Workshop, WALCOM 2016, Kathmandu, Nepal, March 29–31, 2016, Proceedings, Pages pp 181-193, 2016; doi:10.1007/978-3-319-30139-6_15
  12. Biswajit Sanyal, Subhashis Majumder, Wing-Kai Hon, Prosenjit Gupta, Efficient meta-data structure in top-k queries of combinations and multi-item procurement auctions, Theoretical Computer Science (2020) Vol. 814, 210-222. doi:10.1016/j.tcs.2020.01.036
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  14. Matthew Saponaro and Keith Decker, Analysis of Meta-level Communication for Distributed Resource Allocation Problems, AAMAS '17 Proceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems, pp. 1728-1730.
  15. Sapounakis, A.; Tasoulas, I.; Tsikouras, P. Ordered trees and the inorder traversal. Discrete Math. 306 (2006), no. 15, 1732-1741.
  16. A. Sapounakis, I. Tasoulas and P. Tsikouras, "On the Dominance Partial Ordering of Dyck Paths", J. Integer Sequences, Volume 9, 2006, Article 06.2.5.
  17. A. Sapounakis, I. Tasoulas and P. Tsikouras, Counting strings in Dyck paths, Discrete Math., 307 (2007), 2909-2924.
  18. A. Sapounakis, I. Tasoulas, P. Tsikouras, Enumeration of strings in Dyck paths: A bijective approach, Discrete Mathematics, Volume 309, Issue 10, 28 May 2009, Pages 3032-3039.
  19. A. Sapounakis and P. Tsikouras, "On k-colored Motzkin words", J. Integer Sequences, Volume 7, 2004, Article 04.2.5.
  20. Sapounakis, A.; Tsikouras, P. Counting peaks and valleys in k-colored Motzkin paths. Electron. J. Combin. 12 (2005), Research Paper 16, 20 pp.
  21. Aristidis Sapounakis, Panagiotis Tsikouras, Ioannis Tasoulas, Kostas Manes, Strings of Length 3 in Grand-Dyck Paths and the Chung-Feller Property, Electr. J. Combinatorics, 19 (2012), #P2.
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  24. T. Sasao and J. T. Butler, Applications of Zero-Suppressed Decision Diagrams, Synthesis Lectures on Digital Circuits and Systems, November 2014, 123 pages, doi:10.2200/S00612ED1V01Y201411DCS045
  25. Ulrike Sattler, Decidable classes of formal power series with nice closure properties, Diplomarbeit im Fach Informatik, Univ. Erlangen - Nuernberg, Jul 27 1994.
  26. Pratik Saturi, Back to society, Masters thesis, Unitec Institute of Technology (New Zealand, 2019). PDF (A000045)
  27. J. Sauerberg and L. Shu, The long and the short on counting sequences, Amer. Math. Monthly 104 (1997), no. 4, 306-317.
  28. Cédric Saule, Mireille Regnier, Jean-Marc Steyaert, Alain Denise, Counting RNA pseudoknotted structures (extended abstract), dmtcs:2834 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
  29. Arnold Saunders, A Class of Random Recursive Tree Algorithms with Deletion, arXiv:1906.02720 [math.PR], 2019. (A001405)
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  33. Carla D. Savage and Herbert S. Wilf, Pattern avoidance in compositions and multiset permutations (2005), arXiv:math/0504310.
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  88. Raphael Schumacher, The Formulas for the Distribution of the 3-Smooth, 5-Smooth, 7-Smooth and all other Smooth Numbers, arXiv preprint arXiv:1608.06928, 2016
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