Research

My main areas of interest are enumerative and algebraic combinatorics. I particularly enjoy taking a beautiful piece of permutation combinatorics and extending it to other reflection groups or to matrices over finite fields. See below for lists of my research papers, my other publications, papers by students working under my mentorship, and my coauthors.

Papers and preprints

My papers are available on the arXiv or via MathSciNet; arXiv versions are not necessarily equivalent to the published version (sorry). * = student collaborator.

• Garsia–Remmel q-rook numbers are not always unimodal (with A.H. Morales). arXiv:2410.19714
• A Random Card Shuffling Process (with M. Rai*). Involve 17 (2024), no. 4, 603–632. arXiv:2206.04614
• GL_n(F_q)-analogues of some properties of n-cycles in S_n. arXiv:2407.20347
• Disarray, reduced words, and 321-avoidance in George groups (with B.E. Tenner). arXiv:2404.06379
• Combinatorial formulas for shifted dual stable Grothendieck polynomials (with E. Marberg). Forum Math. Sigma 12 (2024), Paper e22. arXiv:2209.03551
• Hurwitz Orbits on Reflection Factorizations of Parabolic Quasi-Coxeter Elements (with T. Douvropoulos). Electron. J. Combin. 31 (2024), no. 1, Paper 27. arXiv:2209.00774
• Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements (with T. Douvropoulos and A.H. Morales). J. Alg. 641 (2024), 648–715. arXiv:2209.00066
• Bargain hunting in a Coxeter group (with B.E. Tenner). Ann. Comb. (2023). arXiv:2302.04404, DOI:10.1007/s00026-023-00670-2.
• Coincidences between intervals in two partial orders on complex reflection groups (with J. Wang). arXiv:2310.12265
• Hurwitz numbers for reflection groups III: Uniform formulas (with T. Douvropoulos and A.H. Morales). arXiv:2308.04751
• Monodromy in Kazhdan-Lusztig cells in affine type A (with M. Chmutov and P. Pylyavksyy). Math. Annalen 386 (2023), 1891–1949. arXiv:1706.00471; DOI:10.1007/s00208-022-02434-4
• An affine generalization of evacuation (with M. Chmutov, G. Frieden, D. Kim, and E. Yudovina). Selecta Math. 28 (2022), no. 4, Article 67. arXiv:1806.07429; DOI:10.1007/s00029-022-00779-x
• Hurwitz numbers for reflection groups I: Generatingfunctionology (with T. Douvropoulos and A.H. Morales). Enum. Comb. Appl. 2 (2022), no. 3, Article S2R20. arXiv:2112.03427
• The Hurwitz action in complex reflection groups (with J. Wang). Comb. Theory 2 (2022), no. 1, #12. arXiv:2105.08104
• The tree search game for two players (with R.B. Boppana). Australas. J. Comb. 82 (2022), no. 2, 119–145. arXiv:2008.11543
• Reflection length in the general linear and affine groups (with E.G. DelMas). Comm. Alg. 50 (2022), no. 2, 668–686. arXiv:1803.03070
• The path-free and path-missing complexes of a directed graph (with D. Grinberg and L. Katthän). arXiv:2102.07894
• Enriched set-valued P-partitions and shifted stable Grothendieck polynomials (with E. Marberg). Math. Z. 299 (2021), no. 3–4, 1929–1972. arXiv:1907.10691
• Factorization problems in complex reflection groups (with A.H. Morales). Canadian. J. Math. 73 (2021), no. 4, 899–946. arXiv:1906.11961
• A note on the Hurwitz action on reflection factorizations of Coxeter elements in complex reflection groups. Electron. J. Combin. 27 (2020), no. 2, Paper 54. arXiv:2001.08238
• Rook Theory of the Finite General Linear Group (with A.H. Morales). Exp. Math. 29 (2020), no. 3, 328–346. arXiv:1707.08192
• Scaling limit of soliton lengths in a multicolor box-ball system (with H. Lyu, P. Pylyavskyy, and A. Sen). arXiv:1911.04458
• Computing reflection length in an affine Coxeter group (with J. McCammond, T.K. Petersen, and P. Schwer). Trans. Amer. Math. Soc. 371 (2019), no. 6, 4097–4127. arXiv:1710.06920
• Invariants of GL_n(F_q) in polynomials modulo Frobenius powers (with V. Reiner and D. Stanton). Proc. Roy. Soc. Edinburgh Sect. A 147 (2017), no. 4, 831–873. arXiv:1403.6521
• Absolute order in general linear groups (with J. Huang and V. Reiner). J. Lond. Math. Soc. (2) 95 (2017), no. 1, 223–247. arXiv:1506.03332
• Circuits and Hurwitz action in finite root systems (with V. Reiner). New York J. Math. 22 (2016), 1457–1486. arXiv:1603.05969
• GL_n(F_q)-analogues of factorization problems in the symmetric group (with A.H. Morales). European J. Combin. 58 (2016), 75–95. arXiv:1511.00711
• Combinatorics of diagrams of permutations (with A.H. Morales). J. Combin. Theory Ser. A 137 (2016), 273–306. arXiv:1405.1608
• Reflection factorizations of Singer cycles (with V. Reiner and D. Stanton). J. Algebraic Combin. 40 (2014), no. 3, 663–691. arXiv:1308.1468
• Combinatorial aspects of flashcard games (with N. Li). Ann. Comb. 18 (2014), no. 3, 459–472. arXiv:1210.2419
• Counting matrices over finite fields with support on skew Young diagrams and complements of Rothe diagrams (with A.J. Klein* and A.H. Morales). J. Algebraic Combin. 39 (2014), no. 2, 429–456. arXiv:1203.5804
• Skyscraper numbers (with T. Khovanova). J. Integer Seq. 16 (2013), no. 7, Article 13.7.2. arXiv:1304.6445
• Enumeration of graded (3 + 1)-avoiding posets (with Y.X. Zhang). J. Combin. Theory Ser. A 120 (2013), no. 6, 1305–1327. arXiv:1106.5480
• Generating trees and pattern avoidance in alternating permutations. Electron. J. Combin. 19 (2012), no. 1, Paper 21. arXiv:1005.4046
• Alternating permutations containing the pattern 123 or 321 exactly once. arXiv:1111.0986
• Matrices with restricted entries and q-analogues of permutations (with R.I. Liu, A.H. Morales, G. Panova, S.V. Sam, and Y.X. Zhang). J. Comb. 2 (2011), no. 3, 355–395. arXiv:1011.4539
• Baron Münchhausen redeems himself: bounds for a coin-weighing puzzle (with T. Khovanova). Electron. J. Combin. 18 (2011), no. 1, Paper 37. arXiv:1006.4135
• Pattern avoidance for alternating permutations and Young tableaux. J. Combin. Theory Ser. A 118 (2011), no. 4, 1436–1450. arXiv:0909.4966
• Alternating, pattern-avoiding permutations. Electron. J. Combin. 16 (2009), no. 1, Note 7. arXiv:0805.1964

Other publications

The article

• Affine symmetric group. WikiJournal of Science 4 (2021), no. 1

is the basis for the Wikipedia article on the Affine symmetric group, which was featured on the front page of Wikipedia on October 8, 2023 (Wayback Machine archived copy). Let me know if there's something that really should be included in the Wikipedia version and isn't, as long as it's in keeping with WP's core policies. (Or add it yourself!)

Also, I often attend and present at FPSAC; here are my extended abstracts:

• Combinatorial formulas for shifted dual stable Grothendieck polynomials (with E. Marberg). 35th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2023), 89B.22, Séminaire Lotharingien de Combinatoire, 2023. (talk)
• The Hurwitz action in complex reflection groups (with J. Wang). 33rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2021), 85B.19, Séminaire Lotharingien de Combinatoire, 2021. (poster)
• Hurwitz numbers for reflection groups (with T. Douvropoulos and A.H. Morales). 33rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2021), 85B.66, Séminaire Lotharingien de Combinatoire, 2021. (talk)
• Factorization problems in complex reflection groups (with A.H. Morales). 31st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2019), 82B.57, Séminaire Lotharingien de Combinatoire, 2019. (talk)
• An affine generalization of evacuation (with M. Chmutov, G. Frieden, D. Kim, and E. Yudovina). 31st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2019), 82B.79, Séminaire Lotharingien de Combinatoire, 2019. (poster)
• Computing reflection length in an affine Coxeter group (with J. McCammond, T.K. Petersen, and P. Schwer). 30th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2018), 80B.51, Séminaire Lotharingien de Combinatoire, 2018. (talk)
• GL(n, q)-analogues of factorization problems in the symmetric group (with A.H. Morales). 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), 755–766, Discrete Math. Theor. Comput. Sci. Proc. BC, 2016.(poster)
• Reflection factorizations of Singer cycles (with V. Reiner and D. Stanton). 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 297–308, Discrete Math. Theor. Comput. Sci. Proc. AT, 2014. (talk)
• Combinatorics of diagrams of permutations (with A.H. Morales). 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 703–714, Discrete Math. Theor. Comput. Sci. Proc. AT, 2014. (poster)
• Enumeration of graded (3 + 1)-avoiding posets (with Y.X. Zhang). 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), 57–68, Discrete Math. Theor. Comput. Sci. Proc. AR, 2012. (talk)
• Matrices with restricted entries and q-analogues of permutations (with R.I. Liu, A.H. Morales, G. Panova, S.V. Sam, and Y.X. Zhang). 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 645–656, Discrete Math. Theor. Comput. Sci. Proc. AO, 2011. (talk)
• Pattern avoidance in alternating permutations and tableaux. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 391–402, Discrete Math. Theor. Comput. Sci. Proc. AN, 2010. (talk)

Papers by my students

• Colin Pirillo and Seth Sabar. Hurwitz Orbits of Equal Size. PUMP Journal of Undergraduate Research 5 (2022), 52–64. arXiv:2102.01145
• Gaurav Gawankar, Dounia Lazreq, Mehr Rai, and Seth Sabar. Hurwitz Actions on Reflection Factorizations in Complex Reflection Group G₆. Rose-Hulman Undergraduate Mathematics Journal 22 (2021), no. 2, Article 6. arXiv:2002.05102
• Tyler Minnick, Colin Pirillo, Sarah Racile, and Yueqi Wang. Hurwitz equivalence of reflection factorizations in G₇. arXiv:2110.08371
• Jiayuan Wang. A note on fully commutative elements in complex reflection groups. Discrete Math. 346 (2023), no. 12, 113611. arXiv:2109.09773
• Colin Aitken. Non-degenerate 2 × k × (k + 1) hypermatrices. Linear Multilinear Algebra 67 (2019), no. 4, 697–704. arXiv:1606.04532
• Zachery Peterson. Hurwitz Transitivity of Longer Reflection Factorizations in G4 and G5. arXiv:1808.01268
• Joshua Alman, Carl Lian, and Brandon Tran. Circular planar electrical networks: posets and positivity. J. Combin. Theory Ser. A 132 (2015), 58–101. arXiv:1309.2697 and arXiv:1309.3011
• Ravi Jagadeesan. Ascent-descent Young diagrams and pattern avoidance in alternating permutations. Electron. J. Combin. 21 (2014), no. 3, Paper 3.9. arXiv:1301.6796
• Nihal Gowravaram and Ravi Jagadeesan. Beyond alternating permutations: pattern avoidance in Young diagrams and tableaux. Electron. J. Combin. 20 (2013), no. 4, Paper 17. arXiv:1301.6796

My collaborators and coauthors

(Apologies to anyone I've missed, misspelled, misalphabetized, or mislinked – please send corrections.)