2025​

 

The nonsymmetric shuffle theorem 

arXiv: 2509.24040

joint with Mark Haiman, Jonah Blasiak, Jennifer Morse and George H. Seelinger

​

Minimal elements in the skew extended 0-Hecke poset 

arXiv: 2509.05918

joint with Nadia Lafrenière, Rosa Orellana, Sheila Sundaram, Stephanie van Willigenburg, and Tamsen Whitehead McGinley

 

​​

Flagged LLT polynomials, nonsymmetric plethysm, and nonsymmetric Macdonald polynomials

arXiv: 2506.09015

joint with Mark Haiman, Jonah Blasiak, Jennifer Morse and George H. Seelinger 

 

​

Dens, nests and the Loehr-Warrington conjecture

J. Amer. Math. Soc., Vol 38, Number 4, June 2025, Pages 1049 – 1106

joint with Mark Haiman, Jonah Blasiak, Jennifer Morse and George H. Seelinger

​

​

The skew immaculate Hecke poset and 0-Hecke modules

Electron. J. Combin.,  Vol 32, Number 2, 2025, #P2.11

joint with Nadia Lafrenière, Rosa Orellana, Sheila Sundaram, Stephanie van Willigenburg, and Tamsen Whitehead McGinley

​

​

A raising operator formula for Macdonald polynomials

Forum of Mathematics. Sigma, 13 (2025), p. e47

joint with Mark Haiman, Jonah Blasiak, Jennifer Morse and George H. Seelinger

​​

​

On the correspondence between integer sequences and vacillating tableaux Enumerative Combinatorics and Applications, Vol 5, Number 1, 2025, #S2R7

joint with Zhanar Berikkyzy, Pamela E. Harris, Catherine Yan and Chenchen Zhao

​

​​​​​

​2024

​

On the Limiting Vacillating Tableaux for Integer Sequences

Journal of Combinatorics, Vol 15, Number 3, 2024, Pages 383 – 400

joint with Zhanar Berikkyzy, Pamela E. Harris, Catherine Yan and Chenchen Zhao

​​

​

Demazure crystals and the Schur positivity of Catalan functions

Inventiones mathematicae, 236, 483 – 547 (2024)

joint with Jonah Blasiak and Jennifer Morse

​

​

Combinatorial Identities for Vacillating Tableaux 

Integers, 24A, #A4 (2024)

joint with Zhanar Berikkyzy, Pamela E. Harris, Catherine Yan and Chenchen Zhao

​

​

LLT polynomials in the Schiffmann algebra

Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2024, no. 811, 2024, pp. 93 – 133.

joint with Mark Haiman, Jonah Blasiak, Jennifer Morse and George H. Seelinger​

​

​

2023

​​

A Catalanimal formula for Macdonald polynomials (Extended Abstract)​

Seminaire Lotharingien de Combinatoire 89B (2023) Article #85, 12 pp., Proceedings of the 35th Conference on Formal Power Series and Algebraic Combinatorics (Davis)

joint with Mark Haiman, Jonah Blasiak, Jennifer Morse and George H. Seelinger

​

​

​A proof of the Extended Delta Conjecture

Forum of Mathematics. Pi, 11 (2023), no. e6, 28

joint with Mark Haiman, Jonah Blasiak, Jennifer Morse and George H. Seelinger

​

​A Shuffle Theorem for Paths Under Any Line

Forum of Mathematics. Pi, 11 (2023), no. e5, 38

joint with Mark Haiman, Jonah Blasiak, Jennifer Morse and George H. Seelinger

​​

​

2021

​

Distribution properties for t-hooks in partitions

Annals of Combinatorics, 25(3), 677 – 695 (2021)

joint with William Craig

​

A note on the Higher order Turán inequalities for k-regular partitions

Research in Number Theory, 7 (2021), no. 1, Paper No. 5, 7 pp.

joint with William Craig

​

​Note: Hermite's criterion on page 2 is not stated correctly. It should be "f  is hyperbolic if and only if M(f) is positive definite." The error has no bearing on any results in the paper.

​​

​

2020

​​

Higher order Turán inequalities for k-regular partitions(Extended Abstract)

Seminaire Lotharingien de Combinatoire 84B (2020), Proceedings of the 32nd Conference on Formal Power Series and Algebraic Combinatorics (Online) 2020, Article 21.

​joint with William Craig

​

​​

k-Schur expansions of Catalan functions

Advances in Mathematics, Vol 371, 16 September 2020, 107209​

joint with Jonah Blasiak, Jennifer Morse and Daniel Summers

​​

​

​2019​

​

Catalan functions and k-Schur positivity

J. Amer. Math. Soc., Vol 32, Number 4, October 2019, Pages 921 – 963

joint with Jonah Blasiak, Jennifer Morse and Daniel Summers

​​

​

2016

​​

On Decomposition of the Product of Demazure Atoms and Demazure Characters arXiv: 1606.02291

 

Decomposition of the product of a monomial and a Demazure atom

Discrete Math. Theor. Comput. Sci., Proceedings of the FPSAC 2016 conference, volume (2016), 1015 – 1026.

 

​

2012

​​

A geometric proof of a theorem on antiregularity of generalized quadrangles

Designs, Codes and Cryptography (2012), 64, 255 – 263.

joint with Dr. Philip Pit Wang Wong​​​​​