Papers etc. by Alexander Yong

My papers on the Mathematics ArXiV.

42. Critique of Hirsch's citation index: a combinatorial Fermi problem preprint (10 pages+appendix), accepted to Notices of the AMS , version of February 13, 2014

41. Polynomials for symmetric orbit closures in the flag variety (with Benjamin Wyser), preprint (5 pages), version of October 27, 2013. 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), preprint (45 pages), version of August 29, 2013.

37. Combinatorial rules for three bases of polynomials (with Colleen Ross), preprint (9 pages), version of February 1, 2013.

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), preprint, 2007 (revised July 2013). 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.

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.