papers by topic

papers (by topic, or chronological)

on arxiv, on google scholar, on mathscinet

Standard Young tableaux and Schubert polynomials


34. On the Okounkov-Olshanski formula for standard tableaux of skew shapes, with Daniel G. Zhu, 2020, arxiv:2007.05006, 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


29. Asymptotics of principal evaluations of Schubert polynomials for layered permutations, with Igor Pak and Greta Panova, 2018, arxiv:1805.04341, accepted Proceedings of the American Mathematical Society


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


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? to appear American Mathematical Monthly


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


25. Rook theory of the finite general linear group, with Joel Brewster Lewis, 2017, arxiv:1707.08192, Experimental Mathematics, 2018, link


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

Flow polytopes and Kostant partition functions


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, accepted Annals of Combinatorics


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, accepted Transactions of the American Mathematical Society


26. Volumes and Ehrhart polynomials of flow polytopes, with Karola Mészáros, 2017, arxiv:1710.00701, accepted Mathematische Zeitschrift.


22. Flow polytopes and the space of diagonal harmonics, with Ricky I. Liu and Karola Mészáros, 2016, arxiv:1610.08370, accepted Canadian Journal of Mathematics


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, submitted


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


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


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


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


30. Combinatorial aspects of the Legendre and Fourier transforms in perturbative quantum field theory, with David M. Jackson and Achim Kempf, arxiv:1805.09812, version with better figures.


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

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

Combinatorics of colored factorizations, flow polytopes, and matrices over finite fields, thesis, MIT 2012

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.