Papers etc. by Alexander Yong

My papers on the Mathematics ArXiV.

83. Representations from matrix varieties, and filtered RSK (with Abigail Price and Ada Stelzer), preprint version of Mar 15, 2024.

82. Combinatorial Commutative Algebra Rules (with Ada Stelzer), preprint version of June 1, 2023. 81. Schubert determinantal ideals are Hilbertian (with Ada Stelzer), preprint version of May 21, 2023. 80. Levi-spherical Schubert varieties (with Yibo Gao and Reuven Hodges), version of December 5, 2023, to appear in Adv. Math. 79. Schubert geometry and combinatorics (with Alexander Woo), preprint version of March 2, 2023 78. Presenting the cohomology ring of a Schubert variety: proof of the minimality conjecture (with Avery St. Dizier), preprint version of August 30, 2022. Accepted to J. London. Math. Soc., 2023. 77. Classifying Levi-spherical Schubert varieties (with Yibo Gao and Reuven Hodges), FPSAC 2022 conference proceedings. Version of March 29, 2022 76. Combinatorics of Newell-Littlewood numbers (with Shiliang Gao, Gidon Orelowitz, and Nicolas Ressayre), FPSAC 2022 conference proceedings. Version of March 29, 2022 75. Minimal equations for Matrix Schubert varieties (with Shiliang Gao), preprint, version of January 17, 2022. 74. Newell-Littlewood numbers III: eigencones and GIT-semigroups (with Shiliang Gao, Gidon Orelowitz, Nicolas Ressayre), preprint, version of July 5, 2021. Accepted to Compositio Math. 73. Castelnuovo-Mumford regularity and Schubert geometry, draft, version of June 8, 2021. 72. Classification of Spherical Schubert varieties (with Yibo Gao and Reuven Hodges), preprint, version of June 6, 2022. To appear in Selecta Math., 2023. 71. The "Grothendieck to Lascoux" conjecture (with Vic Reiner), preprint, version of February 18, 2021. 70. The Kostka semigroup and its Hilbert basis (with Shiliang Gao, Joshua Kiers, and Gidon Orelowitz), preprint, version of February 1, 2021. To appear in Enumerative Combinatorics and Applications , September 2023. 69. Proper permutations, Schubert geometry, and randomness (with David Brewster and Reuven Hodges), preprint, version of December 17, 2020. 68. Generalized permutahedra and Schubert calculus (with Avery St. Dizier), preprint, version of October 27, 2020. To appear in Arnold Math J. 67. Newell-Littlewood numbers II: extended Horn inequalities (with Shiliang Gao and Gidon Orelowitz), preprint, version of September 29, 2020. To appear in Algebraic Combinatorics . 66. Coxeter combinatorics and spherical Schubert geometry (with Reuven Hodges), to appear in Journal of Lie Theory, version of December 2, 2021. 65. Multiplicity-free key polynomials (with Reuven Hodges), preprint, version of July 17, 2020. 64. Newell-Littlewood numbers (with Shiliang Gao and Gidon Orelowitz), Trans. AMS (accepted), version of June 13, 2020. 63. Equivariant cohomology, Schubert calculus, and edge-labeled tableaux (with Colleen Robichaux and Harshit Yadav), to appear in "Facets of Algebraic Geometry: A Volume in Honour of William Fulton's 80th Birthday", Cambridge University Press, London Mathematical Society Lecture Note Series, preprint version of August 29, 2019. 62. The A.B.C.Ds of Schubert calculus (with Colleen Robichaux and Harshit Yadav), Seminaire Lotharingien de Combinatoire, B85a (2020), 12 pp.

61. An estimation method for game complexity (with David Yong), preprint, version of January 29, 2019.

60. Reduced words, complexity, and randomization (with Cara Monical and Benjamin Pankow), preprint, version of January 30, 2019. 59. An efficient algorithm for deciding vanishing of Schubert polynomial coefficients (with Anshul Adve and Colleen Robichaux), Advances in Math., to appear, 2021. 58. Complexity, Newton polytopes, and Schubert polynomials (with Anshul Adve and Colleen Robichaux), Proceedings of the 31st Conference on Formal Power Series and Algebraic Combinatorics (Ljubljana), Sem. Lothar. Combin. 82B (2020), Art. 52, 12 pp. 57. Tropicalization, symmetric polynomials, and complexity (with Alexander Woo), accepted to Journal of Symbolic Computation, version of October 9, 2017. 56. K-orbits and Barbasch-Evens-Magyar varieties (with Laura Escobar and Benjamin Wyser), preprint, version of July 2022. Accepted to Pacific J. Math in 2022. 55. Vanishing of Littlewood-Richardson polynomials is in P (with Anshul Adve and Colleen Robichaux), to appear in Computational Complexity; version of March 21, 2019. 54. Symmetric group representations and Z (with Anshul Adve), C. R. Math. Acad. Sci. Paris 356 (2018), no. 1, 1--4. (Version of June 30, 2017.) 53. Newton polytopes and symmetric Grothendieck polynomials (with Laura Escobar), C. R. Math. Acad. Sci. Paris 355 (2017), no. 8, 831--834. (Version of May 22, 2017.) 52. Newton polytopes in algebraic combinatorics (with Cara Monical and Neriman Tokcan), to appear in Selecta Math, 2019. 51. Governing singularities of symmetric orbit closures (with Alexander Woo and Benjamin Wyser), Algebra and Number theory 12 (2018), no. 1, 173-225. 50. Partition identities and quiver representations (with Richard Rimanyi and Anna Weigandt), J. Algebraic Comb. 47 (2018), no. 1, 129--169. (Version of June 1, 2017). 49. Rhombic tilings and Bott-Samelson varieties (with Laura Escobar, Oliver Pechenik and Bridget Tenner), Rhombic tilings and Bott-Samelson varieties. Proc. Amer. Math. Soc. 146 (2018), no. 5, 1921--1935. (Version of Jun 9, 2016.) 48. Poset edge densities, nearly reduced words and barely set-valued tableaux (with Victor Reiner and Bridget Tenner), to appear in J. Combinatorial Theory Series A, March 13, 2018. 47. Genomic Tableaux (with Oliver Pechenik), J. Algebraic Combinatorics, to appear, version of March 28, 2016. 46. The prism tableau model for Schubert polynomials (with Anna Weigandt), J. Combin. Theory Ser. A 154 (2018), 551--582. (Version of September 8, 2015.) 45. Equivariant K-theory of Grassmannians II: the Knutson-Vakil conjecture (with Oliver Pechenik), to appear in Compositio Math., version of August 3, 2015. 44. Equivariant K-theory of Grassmannians (with Oliver Pechenik), preprint, June 5, 2015; accepted to Forum of Math, Pi. 43. Genomic Tableaux and Combinatorial K-theory (with Oliver Pechenik) to appear in the Proceedings of Formal Power Series and Algebraic combinatorics 2015 , version of April 8, 2015. 42. Critique of Hirsch's citation index: a combinatorial Fermi problem preprint (10 pages+appendix), accepted to Notices of the AMS , version of October 13, 2014. 41. Polynomials for symmetric orbit closures in the flag variety (with Benjamin Wyser), preprint (22 pages), version of September 30, 2014. 40. The Joseph Greenberg problem: combinatorics and comparative linguistics , preprint (6 pages), version of October 10, 2013.

39. Polynomials for GLp x GLq orbit closures in the flag variety (with Benjamin Wyser), to appear in Selecta Math (25 pages), version of March 4, 2014.

38. Root-theoretic Young diagrams and Schubert calculus: planarity and the adjoint varieties (with Dominic Searles), J. Algebra to appear (45 pages), version of August 29, 2013.

37. Combinatorial rules for three bases of polynomials (with Colleen Ross), Seminaire Lotharingien de Combinatoire (11 pages), 2015.

36. Eigenvalues of Hermitian matrices and equivariant cohomology of Grassmannians (with David Anderson and Edward Richmond), accepted to Compositio Math (14 pages), version of April 2, 2013.

35. Singularities of Richardson varieties (with Allen Knutson and Alexander Woo), Math. Res. Letters (10 pages), version of September 14, 2012.

34. Equivariant Schubert calculus and jeu de taquin (with Hugh Thomas), Annales de l'Institut Fourier (31 pages), accepted pending minor revisions, version of July 11, 2012.

33. Patch ideals and Peterson varieties (with Erik Insko), Transformation Groups (23 pages), version of February 3, 2012.

32. Kazhdan-Lusztig polynomials and drift configurations (with Li Li), Algebra and Number Theory , (25 pages), June 19, 2010.

31. Some degenerations of Kazhdan-Lusztig ideals and multiplicities of Schubert varieties (with Li Li), Advances in Math , (31 pages), version of July 1, 2011.

30. K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux (with Edward Clifford and Hugh Thomas), to appear in J. Reine Angew Math (Crelle) (13 pages), Feb 15, 2012.

29. A Grobner basis for Kazhdan-Lusztig ideals (with Alexander Woo), preprint (40 pages), American J. Math , 2012.

28. The direct sum map on Grassmannians and Jeu de taquin for increasing tableaux (with Hugh Thomas), International Math. Res. Notices, (20 pages), 2010.

27. Presenting the cohomology of a Schubert variety (with Victor Reiner and Alexander Woo), Transactions of the AMS, (22 pages), 2009.

26. An approximation algorithm for contingency tables (with Alexander Barvinok, Zur Luria and Alex Samorodnitsky), accepted to Random Structures and Algorithms , 2009 (45 pages).

25. Longest strictly increasing subsequences, Plancherel measure and the Hecke insertion algorithm (with Hugh Thomas), Advances in Applied Math (Dennis Stanton special issue) (34 pages), 10/02/02. (Contains an appendix with Ofer Zeitouni and myself.)
Companion Maple code HeckeLIS.v0.1.txt.

24. A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus (with Hugh Thomas), Algebra and Number Theory , 2008 (22 pages).

23. An S_3 symmetric Littlewood-Richardson rule (with Hugh Thomas), Mathematical Research Letters , volume 15, no.5-6, 2008; (9 pages).

22. Counting magic squares in quasi-polynomial time (with Alexander Barvinok and Alexander Samorodnitsky), preprint (30 pages), 2007.
Companion Maple code contingency.txt. Here is a supplemental webpage comparing various ways of enumerating contingency tables and magic squares.

21. Cominuscule tableau combinatorics (with Hugh Thomas), (revised July 2013). To appear in MSJ-SI 2012 Proceedings. Here is the Maple code to check Lemma 2.4 for Lie types E6 and E7.

20. What is a Young tableau?
Notices of the AMS , Volume 54, Number 2, February 2007.

19. A combinatorial rule for (co)minuscule Schubert calculus (with Hugh Thomas), Advances in Math , 2009.
Companion Maple code cominrule.v1.0.txt. Here's an extra note about comparing cominrule.v1.0.txt with Schubert.v0.2.txt, given below.

18. Stable Grothendieck polynomials and K-theoretic factor sequences (full version) (with A. Buch, A. Kresch, M. Shimozono and H. Tamvakis), Math. Annalen, volume 340, number 2, 2008.

17. Tableau complexes (with A. Knutson and E. Miller), Israel Journal of Math , 163 (2008), 317-343.

16. Multiplicity-free Schubert calculus (with H. Thomas), Canadian Math. Bulletin, 2007.

15. Governing singularities of Schubert varieties (with A. Woo), accepted Journal of Algebra (section on computational algebra), 2007.
Companion Macaulay 2 code Schubsingular.v0.2.m2

Update (Nov 11, 2006): 1. My coauthor A. Woo has extended the interval pattern avoidance ideas of the above paper here.

Update (April 6, 2007): N. Perrin has proved our Gorenstein locus conjecture for the case of minuscule G/P flag varieties. See this paper.

Correction (October, 2019): Example 6.18 has a typo; the multiplicity is 3 (as confirmed by the code, and consistent with Proposition 6.21). We thank Jordan Lambert for bringing this to our attention.

14. Grobner geometry of vertex decompositions and of flagged tableaux (with A. Knutson and E. Miller), Journal fur die reine und angewandte Mathematik (Crelle's Journal) , accepted, 2007.

13. When is a Schubert variety Gorenstein? (with A. Woo),
Advances in Math , Vol 207 (2006), Issue 1 205--220. Companion Maple code available.

12. Grobner geometry of Schubert transition formulae and Littlewood-Richardson rules (with A. Knutson), preprint.

11. A formula for K-theory truncation Schubert calculus (with A. Knutson),
International Mathematics Research Notices , 70 (2004), 3741-3756.

10. Lecture notes on the K-theory of the flag variety and the Fomin-Kirillov quadratic algebra (with C. Lenart), 2004.

9. Quiver coefficients are Schubert structure constants (with A. Buch and F. Sottile),
Mathematical Research Letters , Volume 12, Issue 4, 567-574 (2005).

8. Grothendieck polynomials and Quiver formulas (with A. Buch, A. Kresch and H. Tamvakis),
American Journal of Math , 127 (2005), 551-567.

7. On Combinatorics of Degeneracy Loci and H*(G/B), a dissertation submitted to the Rackham graduate school, University of Michigan, 2003. Companion Maple code for part 2 available. (Includes an implementation of the classical Monk-Chevalley formula for arbitrary Lie type.)

6. On Combinatorics of Quiver Component Formulas,
Journal of Algebraic Combinatorics , 21, 351-371, 2005.

5. Schubert polynomials and Quiver formulas (with A. Buch, A. Kresch and H. Tamvakis),
Duke Math Journal , Volume 122, Issue 1, 125-143 (2004).

4. Degree bounds in quantum Schubert calculus
Proceedings of the AMS , Volume 131, Number 9, 2649-2655 (2003).

3. Tree-like properties of cycle factorizations (with I.P. Goulden)
Journal of Combinatorial Theory Series A, 98 , 106-117 (2002).

2. Dyck paths and a bijection for multisets of hook numbers (with I.P. Goulden),
Discrete Math, 254 , no.1-3, 153-164 (2002).

1. Seeing the factorizations for the trees, M.Math. thesis (1999), University of Waterloo. Available upon request.

More software

(Code for a particular paper is found with the .ps file above.)

  • Maple 7 code to compute Schubert calculus in G/B , website exclusive, 2006.
  • C++ code for estimating permanents, hafnians and the number of forests in a graph, 2003.