Coxeter groups and Hecke algebras
Deograms, distinguished subexpressions, Bruhat order, rational Catalan objects, and Hecke-algebraic methods.
Hello! I am Minho Song, a postdoctoral researcher in the Department of Mathematics at Yonsei University, working under the mentorship of Joonkyung Lee. My research is in algebraic and enumerative combinatorics, especially at its interfaces with algebra and topology. My current interests include Coxeter and Catalan combinatorics, Hecke and skein algebras, and knot theory. I also work on symmetric functions and representation theory, orthogonal polynomials, Riordan groups, and algebraic graph theory. More recently, I have been exploring AI for mathematics, with particular interest in tools for conjecture discovery, computational experimentation, and structural exploration.
Deograms, distinguished subexpressions, Bruhat order, rational Catalan objects, and Hecke-algebraic methods.
Grothendieck polynomials, Schur positivity, refined bases, and related representations.
Braid combinatorics, knot invariants, torus knots, and algebraic and diagrammatic methods.
Moments, reciprocity, lattice-path models, orthogonal polynomials on the unit circle, and generalized families of type RII.
Group and Lie structures, matrix methods, total positivity, and combinatorial reciprocity.
Spectral invariants, Perron values, Kemeny's constant, Braess edges, and acyclic orientations.
Preprint · 2026
With Younggwang Cho, Donghyun Kim, Jang Soo Kim, Hojoon Lee, and Jing Liu.
arXiv:2606.14241The Ramanujan Journal · 2025
With Jihyeug Jang.
Journal articleAdvances in Mathematics · 2024
With Byung-Hak Hwang, Jihyeug Jang, Jang Soo Kim, and U-Keun Song.
arXiv:2104.04251Recent workshops, collaborative projects, and computational experiments in AI for mathematics.
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