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My general research area is combinatorics, grouped broadly into some areas below.
A reduced word graph and its directed quotient by commutations.
The descent statistic on cyclic permutations of fifteen elements.
Reflection Groups and Coxeter Groups
"A ChatGPT-assisted triangle characterization of affine permutation inversion graphs" (with S. C. Billey and H. Chau), under review (2026).
"Descent sets of cyclic permutations in types B and D," under review (2026).
"Commutation classes of reduced words and higher Bruhat orders for affine permutations" (with S. C. Billey and H. Chau) accepted to Séminaire Lotharingien de Combinatoire (2026).
"Descents and flag major index on conjugacy classes of colored permutation groups without short cycles" (with M. Yin), published in Electronic Journal of Combinatorics (2025).
"Descents and flag major index on conjugacy classes of Snr without short cycles" (with M. Yin), published in Séminaire Lotharingien de Combinatoire (2025).
"Moments of colored permutation statistics by conjugacy class," (with J. Campion Loth, M. Levet, S. Sundaram, and M. Yin), published in Annals of Combinatorics (2025).
"Colored permutation statistics by conjugacy class," (with J. Campion Loth, M. Levet, S. Sundaram, and M. Yin) published in Séminaire Lotharingien de Combinatoire (2024).
A flip graph on planar layouts of a planar tanglegram.
A flip graph on the pairs of disjoint triangulations of a pentagon.
Trees and Tanglegrams
"The flip graph on planar layouts of a planar tanglegram is almost a hypercube," published in Discrete Mathematics (2026).
"Reconstruction of caterpillar tanglegrams" (with A. Clifton, E. Czabarka, S. Loeb, U. Okur, L. Szekely, and K. Wicke), published in Discrete Applied Mathematics (2026).
"Decks of rooted binary trees" (with A. Clifton, E. Czabarka, A. Dossou-Olory, S. Loeb, U. Okur, L. Szekely, K. Wicke) published in European Journal of Combinatorics (2025).
"Characterizing planar tanglegram layouts and applications to edge insertion problems," published in Electronic Journal of Combinatorics (2023).
"Sampling planar tanglegrams and pairs of disjoint triangulations" (with A. Black, A. McDonough, G. Nelson, M. Wigal, M. Yin, and Y. Yoo), published in Advances in Applied Mathematics (2023).
"Planar tanglegram layouts and single edge insertion," published in Séminaire Lotharingien de Combinatoire (2022).
A family of graphs realizing the Nordhaus-Gaddum sum upper bound for PSD zero forcing.
Zero Forcing
"New Structures and their Applications to Variants of Zero Forcing and Propagation Time" (with L. Hogben, M. Hunnell, H. Schuerger, B. Small, and Y. Zhang), accepted to Electronic Journal of Combinatorics (2025).
"Upper bounds for positive semidefinite propagation time" (with L. Hogben, M. Hunnell, H. Schuerger, B. Small, and Y. Zhang), published in Discrete Mathematics (2022).
"Using Markov chains to determine expected propagation time for probabilistic zero forcing" (with Y. Chan, E. Curl, J. Geneson, L. Hogben, I. Odegard, and M. Ross), published in Electronic Journal of Linear Algebra (2020).
As a graduate student at the University of Washington, I also worked as a mentor for some excellent undergraduates in the Washington eXperimental Mathematics Laboratory. Our resulting papers are given below.
Graphs with four boundary vertices.
Conjectured minimal configuration for the cosine sign correlation when n=4.
Characterizing Graphs with Small Boundary
"A characterizion of graphs with at most four boundary vertices" (with N. Chiem, W. Dudarov, C. Lee, and S. Lee), published in Journal of Combinatorics (2024).
Extremal Closed Geodesics on the Torus
"Cosine sign correlation" (with S. Dou, A. Goh, M. Legate, and G. Pettigrew), published in Journal of Fourier Analysis and Applications (2024).
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