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Standard Young tableaux and Schubert polynomials
Standard Young tableaux and Schubert polynomials
50. Grothendieck Shenanigans: Permutons from pipe dreams via integrable probability, with Greta Panova, Leonid Petrov, and Damir Yeliussizov, 2024, arxiv:2407.21653
48. Minimal skew semistandard tableaux and the Hillman--Grassl correspondence, with Greta Panova and GaYee Park, 2023, arxiv:2311.09209, accepted Advances in Applied Mathematics
related extended abstract, at FPSAC Davis 2023
39. Hook formulas for skew shapes IV. Increasing tableaux and factorial Grothendieck polynomials, with Igor Pak and Greta Panova, arXiv:2108.10140, Journal of Mathematical Sciences (Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI)), Vol 261 (2022), 630-657,
37. Bijections and hidden symmetries for skew staircase shapes, with Zachary Hamaker, Igor Pak, Luis Serrano, and Nathan Williams, arxiv:2103.09551, Algebraic Combinatorics, Vol 6 (2023) no. 4, 1095-1118.
34. On the Okounkov-Olshanski formula for standard tableaux of skew shapes, with Daniel G. Zhu, 2020, arxiv:2007.05006, Combinatorial Theory, Vol 2 (2022)
related extended abstract, poster at FPSAC 2020 Online
33. Counting linear extensions of posets with determinants of hook lengths, with Alexander Garver, Stefan Grosser, and Jacob Matherne, arxiv:2001.08822, SIAM Journal of Discrete Math (SIDMA), Vol 35 (2021), 205-233.
29. Asymptotics of principal evaluations of Schubert polynomials for layered permutations, with Igor Pak and Greta Panova, 2018, arxiv:1805.04341, Proceedings of the American Mathematical Society, Vol 147 (2019), 1377-1389
28. Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings, with Igor Pak and Martin Tassy, 2018, arxiv:1805.00992, Combinatorics Probability and Computing, Vol 31 (2022), 550-573.
24. Hook formulas for skew shapes III. Multivariate and product formulas, with Igor Pak and Greta Panova, 2017, arxiv:1707.00931, Algebraic Combinatorics, Vol 2 (2019), 815-861, poster
21. Asymptotics for the number of standard Young tableaux of skew shape, with Igor Pak and Greta Panova, 2016, arxiv:1610.07561, to appear European Journal of Combinatorics,
related article: Why is π < 2φ?, American Mathematical Monthly, Vol 125 (2018), 715-723.
20. Hook formulas for skew shapes II. Combinatorial proofs and enumerative applications, with Igor Pak and Greta Panova, 2016, arxiv:1610.04744, SIAM Journal of Discrete Math (SIDMA), Vol 31 (2017), 1953–1989.
18. Hook formulas for skew shapes I. q-analogues and bijections, with Igor Pak and Greta Panova, 2015, arxiv:1512.08348, code, Journal of Combinatorial Theory Series A, Vol 154 (2018), 350-405
Rook placements and q-analogues
Rook placements and q-analogues
51. Garsia--Remmel q-rook numbers are not always unimodal, with Joel Brewster Lewis, 2024, arxiv:2410.19714
25. Rook theory of the finite general linear group, with Joel Brewster Lewis, 2017, arxiv:1707.08192, Experimental Mathematics, 2018, link, mentioned in Igor Pak's blog
13. Combinatorics of diagrams of permutations, with Joel Brewster Lewis, 2014, arXiv:1405.1608, Journal of Combinatorial Theory Series A, Vol 137 (2016), 273-306, related extended abstract and poster FPSAC Chicago 2014; supplementary code and data (v2. has an appendix by Axel Hultman with a shorter elegant proof of part of Thm. 2.1)
8. Counting matrices over finite fields with support on skew Young diagrams and complements of Rothe diagrams, with Aaron J. Klein and Joel Brewster Lewis, Journal of Algebraic Combinatorics, Vol 39, No 2 (2014) 429-456, arXiv:1203.5804, supplementary code and data
4. Matrices with restricted entries and q-analogues of permutations, with Joel Brewster Lewis, Ricky Liu, Greta Panova, Steven V Sam, Yan Zhang, Journal of Combinatorics, Vol 2, No 3 (2012) 355-396, arXiv:1011.4539; related extended abstract FPSAC Iceland 2011
Chromatic symmetric functions
Chromatic symmetric functions
41. The Newton polytope and Lorentzian property of chromatic symmetric functions, with Jacob Matherne and Jesse Selover, 2022, arXiv:2201.07333
35. Chromatic symmetric functions of Dyck paths and q-rook theory, with Laura Colmenarejo and Greta Panova, 2020, arxiv:2104.07599, (extended abstract arxiv:2012.00913), European Journal of Combinatorics, Vol 107 (2023) 103595.
Polytopes, Flow polytopes and Kostant partition functions
Polytopes, Flow polytopes and Kostant partition functions
52. Skew shapes, Ehrhart positvitiy and beyond, with Luis Ferroni and Greta Panova, arxiv:2503.16403
49. Capacity bounds on integral flows and the Kostant partition function, with Jonathan Leake, 2024, arxiv:2406.07838
46. Generalized Pitman-Stanley polytopes: vertices and faces, with William T. Dugan, Maura Hegarty, and Annie Raymond, arxiv:2307.09925, cocalc
related extended abstract, at FPSAC Davis 2023
45. Realizing the s-permutahedron with flow polytopes, with Rafael S. González D'León, Eva Philippe, Daniel Tamayo, and Martha Yip, arxiv:2307.03474, cocalc
44. Enumeration of max-pooling responses with generalized permutohedra, with Laura Escobar, Patricio Gallardo, Javier González-Anaya, José L. González, Guido Montúfar, 2022, arxiv:2209.14978, github, submitted
38. Column convex matrices, G-cyclic orders, and flow polytopes, with Rafael S. González D'León, Christopher R. H. Hanusa and Martha Yip, arxiv:2107.07326, accepted Discrete and Computational Geometry
36. Refinements and Symmetries of the Morris identity for volumes of flow polytopes, with William Shi, 2021, arxiv:2102.05825, Comptes Rendus Mathématique, Vol 359 (2021), 823-851.
32. Kostant's partition function and magic multiplex juggling sequences, with Carolina Benedetti, Christopher R. H. Hanusa, Pamela E. Harris, Anthony Simpson, arxiv:2001.03219, Annals of Combinatorics, Vol 24 (2020), 439-473
27. A combinatorial model for computing volumes of flow polytopes, with Carolina Benedetti, Rafael S. González D'León, Christopher R. H. Hanusa, Pamela E. Harris, Apoorva Khare, and Martha Yip, 2018, arxiv:1801.07684, Transactions of the American Mathematical Society, 372 (2019), 3369-3404
26. Volumes and Ehrhart polynomials of flow polytopes, with Karola Mészáros, 2017, arxiv:1710.00701, Mathematische Zeitschrift 293 (2019), 1369-1401, link,
22. Flow polytopes and the space of diagonal harmonics, with Ricky I. Liu and Karola Mészáros, 2016, arxiv:1610.08370, Canadian Journal of Mathematics, Vol 71 (2019), 1495-1521
16. On flow polytopes, order polytopes, and certain faces of the alternating sign matrix polytope, with Karola Mészáros and Jessica Striker, 2015, arXiv:1510.03357, Discrete & Computational Geometry, Vol 62 (2019), 128–163
14. The polytope of Tesler matrices, with Karola Mészáros and Brendon Rhoades, 2014, arXiv:1409.8566, B. Selecta Mathematica New Ser., Vol 23 (2017) 425, related extended abstract FPSAC Korea 2015
10. Flow polytopes of signed graphs and the Kostant partition function, with Karola Mészáros, 2012, arXiv:1208.0140, International Mathematics Research Notices, No 3 (2015), 830-871, preprint, related extended abstract FPSAC Japan 2012; supplementary code
Factorizations of permutations (maps) and q-analogues
Factorizations of permutations (maps) and q-analogues
47. Hurwitz numbers for reflection groups III: Uniform formulas, with Theo Douvropoulos and Joel Brewster Lewis, 2023, arXiv:2308.04751,
43. Combinatorial and Algebraic Enumeration: a survey of the work of Ian P. Goulden and David M. Jackson, with Angèle M. Foley, Amarpreet Rattan and Karen Yeats, 2022, arXiv:2209.10075, Algebraic Combinatorics, Vol 5 (2022) no. 6,1205-1226, link
42. Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements, with Theo Douvropoulos and Joel Brewster Lewis, Journal of Algebra, Vol 651 (2024), 648-715, arXiv:2209.00066
40. Hurwitz numbers for reflection groups I: Generatingfunctionology, with Theo Douvropoulos and Joel Brewster Lewis, 2021, arXiv:2112.03427, Enumerative Combinatorics and Applications, Vol 2 (2022) Article #S2R20
31. Factorization problems in complex reflection groups, with Joel Brewster Lewis, arxiv:1906.11961
related extended abstract, FPSAC Slovenia 2019
17. GLn(F_q)-analogues of factorization problems in the symmetric group, with Joel Brewster Lewis, 2015, arxiv:1511.00711, European Journal of Combinatorics, Vol 58 (2016) 75-95 preprint, related extended abstract, FPSAC Vancouver 2016.
15. Probabilistic trees with algebraic roots, with Olivier Bernardi, Electronic Journal of Combinatorics, Vol 23, No 2 (2016), arXiv:1501.01135, code
9. Counting trees using symmetries, with Olivier Bernardi, Journal of Combinatorial Theory Series A, Vol 123, No 1 (2014) 104-122, arXiv:1206.0598
7. Separation probabilities for products of permutations, with Olivier Bernardi, Richard P. Stanley and Rosena R. X. Du, Combinatorics Probability and Computing,Vol 23, No 2 (2014) 201-222, arXiv:1202.6471
6. Bijections and symmetries for the factorizations of the long cycle, with Olivier Bernardi, Advances in Applied Math, Vol 50, No 5 (2013) 702-722, arXiv:1112.4970
5. Bijective evaluation of the connection coefficients of the double coset algebra, with Ekaterina Vassilieva, 2010, arXiv:1011.5001, poster FPSAC Iceland 2011
2. Direct bijective computation of the generating series for 2 and 3-connection coefficients of the symmetric group, with Ekaterina Vassilieva, Electronic Journal of Combinatorics, Vol 20, No 2 (2013), arXiv:1101.3614, related extended abstract FPSAC Austria 2009
Enumeration
Enumeration
11. Structure and enumeration of (3+1)-free posets
with Mathieu Guay-Paquet and Eric Rowland, Annals of Combinatorics, Vol 18, No 4 (2014), 645-674, arXiv:1303.3652, related extended abstract FPSAC France 2013
1. On the group-like behaviour of the Le-Murakami-Ohtsuki invariant, with David M. Jackson and Iain Moffatt, Journal of knot theory and its ramifications, Vol 16, No 6 (2007) 699-718, arXiv:QA/0511452
Connections to physics
Connections to physics
30. Towards a more algebraic footing for quantum field theory, with David M. Jackson and Achim Kempf, arxiv:1805.09812, Journal of Physics A: Mathematical and Theoretical, Vol 54 285201
Note: the title changed from Algebraic combinatorial Fourier and Legendre transforms with applications in perturbative quantum field theory
23. A robust generalization of the Legendre transform for QFT, with David M. Jackson and Achim Kempf, Journal of Physics A: Mathematical and Theoretical, Vol 50 (2017), arxiv:1612.00462, we build on the unpublished preprint arXiv:0810.4293
13. New Dirac Delta function based methods with applications to perturbative expansions in quantum field theory and beyond, with Achim Kempf and David M. Jackson, Journal of Physics A: Mathematical and Theoretical, Vol 47, No 41 (2014), arXiv:1404.0747, related article: How to (path) integrate by differentiating, Achim Kempf, David M. Jackson, Alejandro Morales, J. Phys.: Conf. Ser. 626 (2015), arxiv:1507.04348
update: This methods to integrate by differentiating have been implemented in Maple 2019 to compute Laplace and Fourier transforms and their inverses for a larger class of problems and to speed up other cases.
4. E7(7) constraints on counterterms in N=8 supergravity, with Niklas Beisert, Henriette Elvang, Daniel Z. Freedman, Michael Kiermaier, and Stephan Stieberger, Physics Letters B, Vol 694 No 3 (2010) 265-271,arXiv:1009.1643
Miscellaneous
Miscellaneous
19. Efficient Routing for Cost Effective Scale-Out Data Architectures
with Ashwin Narayan, Vuk Marković, Natalia Postawa, Anna King, Ashwin Kumar, Petros Efstathopoulos, 2016, short paper Proceedings 2016 IEEE MASCOTS, London, 424-429, IEEE:Xplore, arxiv:1606.08884, RIPS 2015 project
Phd thesis
Phd thesis
Combinatorics of colored factorizations, flow polytopes, and matrices over finite fields, thesis, MIT 2012
Lecture notes (not edited by lecturers)
Lecture notes (not edited by lecturers)
Math 206 Combinatorics of words: notes from course by Igor Pak, UCLA Fall 2014
Linear extensions of partially ordered sets: notes from minicourse by Richard Stanley, ECCO 2014, Bogota, June 2014.
- last updated: October 24, 2014
18.318 topics in combinatorics: Positive Grassmannian: typed notes from course by Alex Postnikov, MIT Spring 2012
(all files, images made using ipe, file to install it on a Mac)
- last updated: April 19, 2014
- shorter notes by Zvi Rosen from minicourse by Alex Postnikov in ECCO 2012.
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