Publications Citing Sage-Combinat

SageMath-Combinat is a software project whose mission statement is to improve the open source mathematical system SageMath as an extensible toolbox for computer exploration in (algebraic) combinatorics, and foster code sharing between researchers in this area. SageMath-Combinat is the reincarnation in SageMath of MuPAD-Combinat; see the list of publications citing the latter.

Below is a list of publications citing SageMath-Combinat. This list is also available in BibTeX format. The publications listed in each section are sorted in chronological order. Where two or more items are published in the same year, these items are sorted alphabetically by the authors' last names.

Articles

  1. Dan Drake and Jang Soo Kim. k-distant Crossings and Nestings of Matchings and Partitions. Proceedings of the 21st International Conference on Formal Power Series and Algebraic Combinatorics. Discrete Mathematics & Theoretical Computer Science, volume AK, pages 351--362, 2009.
  2. Ghislain Fourier, Masato Okado, and Anne Schilling. Kirillov-Reshetikhin crystals for nonexceptional types. Advances in Mathematics, volume 222, number 3, pages 1080--1116, 2009.
  3. Tom Denton. A combinatorial formula for orthogonal idempotents in the 0-Hecke algebra of S_N. Proceedings of the 22nd International Conference on Formal Power Series and Algebraic Combinatorics. Discrete Mathematics & Theoretical Computer Science, volume AN, pages 701--712, 2010.
  4. Dan Drake. Bijections from Weighted Dyck Paths to Schröder Paths. Journal of Integer Sequences, volume 13, number 9, pages 10.9.2, 2010.
  5. Ghislain Fourier, Masato Okado, and Anne Schilling. Perfectness of Kirillov-Reshetikhin Crystals for Nonexceptional Types. Contemporary Mathematics, volume 506, pages 127--143, 2010.
  6. Florent Hivert, Anne Schilling, and Nicolas M. Thiéry. The biHecke Monoid of A Finite Coxeter Group. Proceedings of the 22nd International Conference on Formal Power Series and Algebraic Combinatorics. Discrete Mathematics & Theoretical Computer Science, volume AN, pages 307--318, 2010.
  7. Brant Jones and Anne Schilling. Affine Structures and a Tableau Model for E_6 Crystals. Journal of Algebra, volume 324, number 9, pages 2512--2542, 2010.
  8. Thomas Lam, Anne Schilling, and Mark Shimozono. K-theory Schubert Calculus of the Affine Grassmannian. Compositio Mathematica, volume 146, number 4, pages 811--852, 2010.
  9. Jean-Christophe Novelli, Franco Saliola, and Jean-Yves Thibon. Representation theory of the higher-order peak algebras. Journal of Algebraic Combinatorics, volume 32, number 4, pages 465--495, 2010.
  10. Anne Schilling and Qiang Wang. Promotion Operator on Rigged Configurations of Type A. The Electronic Journal of Combinatorics, volume 17, number 1, pages R24, 2010.
  11. Jason Bandlow, Anne Schilling, and Mike Zabrocki. The Murnaghan-Nakayama rule for k-Schur functions. Journal of Combinatorial Theory, Series A, volume 118, number 5, pages 1588--1607, 2011.
  12. Jason Bandlow, Anne Schilling, and Mike Zabrocki. The Murnaghan-Nakayama rule for k-Schur functions. Proceedings of the 23rd International Conference on Formal Power Series and Algebraic Combinatorics. Discrete Mathematics & Theoretical Computer Science, volume AO, pages 99--110, 2011.
  13. Daniel Bump and Maki Nakasuji. Casselman's Basis of Iwahori Vectors and the Bruhat Order. Canadian Journal of Mathematics, volume 63, pages 1238--1253, 2011.
  14. Marie-Claude David and Nicolas M. Thiéry. Exploration of finite dimensional Kac algebras and lattices of intermediate subfactors of irreducible inclusions. Journal of Algebra and Its Applications, volume 10, number 5, pages 995--1106, 2011.
  15. Tom Denton. A combinatorial formula for orthogonal idempotents in the 0-Hecke algebra of the symmetric group. Electronic Journal of Combinatorics, volume 18, number 1, pages P28, 2011.
  16. Tom Denton, Florent Hivert, Anne Schilling, and Nicolas M. Thiéry. On the representation theory of $\mathcal{J}$-trivial monoids. Séminaire Lotharingien de Combinatoire, volume 64, pages B64d, 2011.
  17. A. Blondin Massé, S. Brleka, A. Garona, and S. Labbé. Equations on palindromes and circular words. Theoretical Computer Science, volume 412, number 27, pages 2922--2930, 2011.
  18. Gregg Musiker and Christian Stump. A Compendium on the Cluster Algebra and Quiver Package in Sage. S{é}minaire Lotharingien de Combinatoire, volume 65, pages B65d, 2011.
  19. Steven Pon and Qiang Wang. Promotion and evacuation on standard Young tableaux of rectangle and staircase shape. Electronic Journal of Combinatorics, volume 18, number 1, pages P18, 2011.
  20. Viviane Pons. Multivariate Polynomials in Sage. S{é}minaire Lotharingien de Combinatoire, volume 66, number 7, pages B66z, 2011.
  21. Anne Schilling and Peter Tingley. Demazure crystals and the energy function. Proceedings of the 23rd International Conference on Formal Power Series and Algebraic Combinatorics. Discrete Mathematics & Theoretical Computer Science, volume AO, pages 861--872, 2011.
  22. Marcelo Aguiar, Carlos André, Carolina Benedetti, Nantel Bergeron, Zhi Chen, Persi Diaconis, Anders Hendrickson, Samuel Hsiao, I. Martin Isaacs, Andrea Jedwab, Kenneth Johnson, Gizem Karaali, Aaron Lauve, Tung Le, Stephen Lewis, Huilan Li, Kay Magaard, Eric Marberg, Jean-Christophe Novelli, Amy Pang, Franco Saliola, Lenny Tevlin, Jean-Yves Thibon, Nathaniel Thiem, Vidya Venkateswaran, C. Ryan Vinroot, Ning Yan, and Mike Zabrocki. Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras. Adv. Math., volume 229, number 4, pages 2310--2337, 2012.
  23. Chris Berg, Nantel Bergeron, Steven Pon, and Mike Zabrocki. Expansions of k-Schur Functions in the Affine nilCoxeter Algebra. Electronic Journal of Combinatorics, volume 19, number 2, pages P55, 2012.
  24. Chris Berg, Nantel Bergeron, Hugh Thomas, and Mike Zabrocki. Expansion of k-Schur functions for maximal rectangles within the affine nilCoxeter algebra. J. Comb., volume 3, number 3, pages 563--589, 2012.
  25. Tom Denton. Canonical Decompositions of Affine Permutations, Affine Codes, and Split k-Schur Functions. Electronic Journal of Combinatorics, volume 19, number 4, pages P19, 2012.
  26. Tom Denton. Algebraic and affine pattern avoidance. Sém. Lothar. Combin., volume 69, pages Art. B69c,40, 2012.
  27. Valentin Féray and Pierre-Loïc Méliot. Asymptotics of q-plancherel measures. Probability Theory and Related Fields, volume 152, pages 589--624, 2012.
  28. Kyu-Hwan Lee and Ben Salisbury. A combinatorial description of the Gindikin-Karpelevich formula in type {$A$}. J. Combin. Theory Ser. A, volume 119, number 5, pages 1081--1094, 2012.
  29. Jennifer Morse and Anne Schilling. A combinatorial formula for fusion coefficients. Proceedings of the 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012). Discrete Mathematics & Theoretical Computer Science, volume AR, pages 735--744, 2012.
  30. Steven Pon. Affine Stanley symmetric functions for classical types. Journal of Algebraic Combinatorics, volume 36, number 4, pages 595--622, 2012.
  31. Martin Rubey. Maximal {0}-{$1$}-fillings of moon polyominoes with restricted chain lengths and rc-graphs. Adv. in Appl. Math., volume 48, number 2, pages 290--305, 2012.
  32. Anne Schilling and Peter Tingley. Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function. The Electronic Journal of Combinatorics, volume 19, number 2, pages P4, 2012.
  33. Arvind Ayyer, Steven Klee, and Anne Schilling. Markov chains for promotion operators. Fields Communications Series, Springer, 2013.
  34. I. P. Goulden, Mathieu Guay-Paquet, and Jonathan Novak. Polynomiality of monotone Hurwitz numbers in higher genera. Advances in Mathematics, volume 238, number 1, pages 1--23, 2013.
  35. Florent Hivert, Anne Schilling, and Nicolas M. Thiéry. The biHecke monoid of a finite Coxeter group and its representations. Algebra & Number Theory, volume 7, number 3, pages 595--671, 2013.
  36. Cristian Lenart, Satoshi Naito, Daisuke Sagaki, Anne Schilling, and Mark Shimozono. A uniform model for Kirillov-Reshetikhin crystals. Extended abstract. DMCTS proc, volume AS, pages 25--36, 2013.
  37. Cristian Lenart and Anne Schilling. Crystal energy functions via the charge in types A and C. Mathematische Zeitschrift, volume 273, number 1-2, pages 401--426, 2013.
  38. Masato Okado, Reiho Sakamoto, and Anne Schilling. Affine crystal structure on rigged configurations of type D_n^(1). Journal of Algebraic Combinatorics, volume 37, number 3, pages 571--599, 2013.
  39. Arvind Ayyer, Steven Klee, and Anne Schilling. Combinatorial Markov chains on linear extensions. J. Algebraic Combin., volume 39, number 4, pages 853--881, 2014.
  40. Chris Berg, Nantel Bergeron, Franco Saliola, Luis Serrano, and Mike Zabrocki. A lift of the Schur and Hall-Littlewood bases to non-commutative symmetric functions. Canad. J. Math., volume 66, number 3, pages 525--565, 2014.
  41. Mathieu Guay-Paquet, Alejandro H. Morales, and Eric Rowland. Structure and enumeration of {$(3+1)$}-free posets. Ann. Comb., volume 18, number 4, pages 645--674, 2014.
  42. Kyu-Hwan Lee and Ben Salisbury. Young tableaux, canonical bases, and the Gindikin-Karpelevich formula. J. Korean Math. Soc., volume 51, number 2, pages 289--309, 2014.
  43. Kyu-Hwan Lee, Philip Lombardo, and Ben Salisbury. Combinatorics of Casselman-Shalika formula in type {$A$}. Proc. Amer. Math. Soc., volume 142, number 7, pages 2291--2301, 2014.
  44. Tomoki Nakanishi and Salvatore Stella. Diagrammatic description of {$c$}-vectors and {$d$}-vectors of cluster algebras of finite type. Electron. J. Combin., volume 21, number 1, pages Paper 1.3,107, 2014.
  45. Arvind Ayyer, Anne Schilling, Benjamin Steinberg, and Nicolas M. Thiéry. Directed Nonabelian Sandpile Models on Trees. Comm. Math. Phys., volume 335, number 3, pages 1065--1098, 2015.
  46. Arvind Ayyer, Anne Schilling, Benjamin Steinberg, and Nicolas M. Thiéry. Markov chains, {$ℛ$}-trivial monoids and representation theory. Internat. J. Algebra Comput., volume 25, number 1-2, pages 169--231, 2015.
  47. Chris Berg, Nantel Bergeron, Franco Saliola, Luis Serrano, and Mike Zabrocki. Indecomposable modules for the dual immaculate basis of quasi-symmetric functions. Proc. Amer. Math. Soc., volume 143, number 3, pages 991--1000, 2015.
  48. Darij Grinberg and Tom Roby. Iterative Properties of Birational Rowmotion {II}: Rectangles and Triangles. The Electronic Journal of Combinatorics, volume 22, number 3, pages 3.40, 2015.
  49. Cristian Lenart, Satoshi Naito, Daisuke Sagaki, Anne Schilling, and Mark Shimozono. A uniform model for Kirillov-Reshetikhin crystals I: Lifting the parabolic quantum Bruhat graph. Int. Math. Res. Not. IMRN, number 7, pages 1848--1901, 2015.
  50. Ben Salisbury and Travis Scrimshaw. A rigged configuration model for {$B(\infty)$}. J. Combin. Theory Ser. A, volume 133, pages 29--57, 2015.
  51. Anne Schilling and Travis Scrimshaw. Crystal structure on rigged configurations and the filling map. Electronic J. Combinatorics, volume 22, number 1, pages P1.73, 2015.
  52. Darij Grinberg and Tom Roby. Iterative Properties of Birational Rowmotion I: Generalities and Skeletal Posets. The Electronic Journal of Combinatorics, volume 23, number 1, pages 1.33, 2016.
  53. Seok-Jin Kang, Kyu-Hwan Lee, Hansol Ryu, and Ben Salisbury. A combinatorial description of the affine Gindikin-Karpelevich formula of type $A_n^{(1)}$. Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics. Amer. Math. Soc., Providence, RI, pages 145--165, 2016.
  54. Jennifer Morse and Anne Schilling. Crystal approach to affine Schubert calculus. International Mathematics Research Notices, volume 2016, number 8, pages 2239--2294, 2016.
  55. Ben Salisbury and Travis Scrimshaw. Connecting marginally large tableaux and rigged configurations. Algebr. Represent. Theory, volume 19, number 3, pages 523--546, 2016.
  56. Travis Scrimshaw. A crystal to rigged configuration bijection and the filling map for type {$D_4^{(3)}$}. J. Algebra, volume 448, pages 294--349, 2016.
  57. Mike Zabrocki Chris Berg, Nathan Williams. Symmetries on the Lattice of k-Bounded Partitions. Ann. Comb., volume 20, number 2, pages 251--281, 2016.
  58. Arvind Ayyer, Anne Schilling, and Nicolas M. Thiéry. Spectral gap for random-to-random shuffling on linear extensions. Exp. Math., volume 26, number 1, pages 22--30, 2017.
  59. Emily Gunawan and Travis Scrimshaw. Realization of Kirillov-Reshetikhin crystals {$B^{1,s}$} for {$\widehat{\mathfrak{sl}}_n$} using Nakajima monomials. Sém. Lothar. Combin., volume 78B, pages Art. 47,12, 2017.
  60. Tobias Johnson, Anne Schilling, and Erik Slivken. Local limit of the fixed point forest. Electronic Journal of Probability, volume 22, pages 1--26, 2017.
  61. Masato Okado, Reiho Sakamoto, Anne Schilling, and Travis Scrimshaw. Type {$D_n^{(1)}$} rigged configuration bijection. J. Algebraic Combin., volume 46, number 2, pages 341--401, 2017.
  62. Jianping Pan and Travis Scrimshaw. Virtualization map for the Littelmann path model. Transform. Groups, 2017.
  63. Ben Salisbury and Travis Scrimshaw. Rigged configurations for all symmetrizable types. Electron. J. Combin., volume 24, number 1, pages Paper 1.30,13, 2017.
  64. Ben Salisbury and Travis Scrimshaw. Using rigged configurations to model {$B(\infty)$}. Sém. Lothar. Combin., volume 78B, pages Art. 34,12, 2017.
  65. Anne Schilling. Richard Stanley through a crystal lens and from a random angle. in: The Mathematical Legacy of Richard P. Stanley, AMS 2016, pages 287--299, 2017.
  66. Anne Schilling, Nicolas M. Thiery, Graham White, and Nathan Williams. Braid moves in commutation classes of the symmetric group. European J. Combin., volume 62, pages 15--34, 2017.
  67. Travis Scrimshaw. Rigged configurations as tropicalizations of loop Schur functions. J. Integrable Syst., volume 2, number 1, pages xyw015,24, 2017.
  68. Ben Salisbury and Travis Scrimshaw. Rigged configurations and the {$*$}-involution. Lett. Math. Phys., 2018.

Theses

  1. Nicolas Borie. Calculate invariants of permutation groups by Fourier Transform. PhD thesis, Laboratoire de mathématiques d'Orsay, 2011.
  2. Tom Denton. Excursions into Algebra and Combinatorics at q=0. PhD thesis, Department of Mathematics, 2011.
  3. Viviane Pons. Combinatoire alg{è}brique li{è}e aux ordres sur les permutations. PhD thesis, Marne-la-Valle, 2013.
  4. Travis Scrimshaw. Crystals and rigged configurations. PhD thesis, Department of Mathematics, 2015.

Books

  1. Alexandre Casamayou, Nathann Cohen, Guillaume Connan, Thierry Dumont, Laurent Fousse, François Maltey, Matthias Meulien, Marc Mezzarobba, Clément Pernet, Nicolas M. Thiéry, and Paul Zimmermann. Calcul Mathématique avec Sage. CreateSpace, 2013.
  2. Thomas Lam, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono, and Mike Zabrocki. {k}-Schur functions and affine Schubert calculus. Springer, New York; Fields Institute for Research in Mathematical Sciences, Toronto, ON, 2014.
  3. William Paulsen. Abstract Algebra: An Interactive Approach, 2nd ed.. Chapman and Hall/CRC Press, 2016.
  4. Daniel Bump and Anne Schilling. Crystal Bases: Representations and Combinatorics. World Scientific, 2017.

Preprints

  1. Nicolas M. Thiéry. Algèbre Combinatoire et Effective; des graphes aux algèbres de Kac via l'exploration informatique. Mémoire d'{Ha}bilitation à Diriger des Recherches, 2008.
  2. Nicolas M. Thiéry. Sage-Combinat, Free and Practical Software for Algebraic Combinatorics. Software demonstration, FPSAC'09, Hagenberg, Austria, 2009.
  3. Nicolas Borie and Nicolas M. Thiéry. An evaluation approach to computing invariants rings of permutation groups. arXiv:1110.3849, 2011.
  4. Chris Berg, Nantel Bergeron, Franco Saliola, Luis Serrano, and Mike Zabrocki. Multiplicative structures of the immaculate basis of non-commutative symmetric functions. arXiv:1305.4700, 2013.
  5. James M. Borger. Witt vectors, semirings, and total positivity. arXiv:1310.3013, 2013.
  6. Frédéric Chapoton, Florent Hivert, and Jean-Christophe Novelli. A set-operad of formal fractions and dendriform-like sub-operads. arXiv:1307.0092, 2013.
  7. Andrew Mathas. Cyclotomic quiver Hecke algebras of type A. arXiv:1310.2142, 2013.
  8. Dan Orr and Mark Shimozono. Specializations of nonsymmetric Macdonald-Koornwinder polynomials. arXiv:1310.0279, 2013.
  9. Grégory Chatel Viviane Pons. Counting smaller elements in the Tamari and $m$-Tamari lattices. arXiv:1311.3922, 2013.
  10. Chris Berg, Viviane Pons, Travis Scrimshaw, Jessica Striker, and Christian Stump. FindStat - the combinatorial statistics database. arXiv:1401.3690, 2014.
  11. Cristian Lenart, Satoshi Naito, Daisuke Sagaki, Anne Schilling, and Mark Shimozono. A uniform model for Kirillov-Reshetikhin crystals {II}. Alcove model, path model, and $P=X$. arXiv:1402.2203, 2014.
  12. Jin Hong, Hyeonmi Lee, and Roger Tian. Rigged Configuration Descriptions of the Crystals {$B(\infty)$} and {$B(łambda)$} for Special Linear Lie Algebras. arXiv:1604.04357, 2016.
  13. Mike Zabrocki Rosa Orellana. Symmetric group characters as symmetric functions. arXiv:1605.06672, 2016.
  14. N. Cohen and D. V. Pasechnik. {Implementing Brouwer's database of strongly regular graphs}. arXiv:1601.00181, 2016-01.
  15. Erik Aas, Darij Grinberg, and Travis Scrimshaw. Multiline queues with spectral parameters. arXiv:1810.08157, 2018.

Citing Sage-Combinat

If you use Sage-Combinat in a book, paper, website, etc., please email the webmaster and the Sage-Combinat team. Please reference Sage-Combinat as described here. The preferred way to submit publication details is to provide them as a pull request on the dedicated GitHub repository to update the file Sage-Combinat.bib.
Also, be sure to find out which components of SageMath, e.g. NumPy, PARI, GAP, that your calculation uses and properly attribute those systems. If you are unsure, ask on the sage-support mailing list. Similarly, consider finding out who wrote the SageMath code you are using and acknowledge them explicitly as well.