Minho Song

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.

Portrait of Minho Song

Research interests

Coxeter groups and Hecke algebras

Deograms, distinguished subexpressions, Bruhat order, rational Catalan objects, and Hecke-algebraic methods.

Symmetric functions and representation theory

Grothendieck polynomials, Schur positivity, refined bases, and related representations.

Knot theory and skein algebras

Braid combinatorics, knot invariants, torus knots, and algebraic and diagrammatic methods.

Orthogonal polynomials

Moments, reciprocity, lattice-path models, orthogonal polynomials on the unit circle, and generalized families of type RII.

Riordan groups

Group and Lie structures, matrix methods, total positivity, and combinatorial reciprocity.

Algebraic graph theory

Spectral invariants, Perron values, Kemeny's constant, Braess edges, and acyclic orientations.

Recent directions

All publications

Preprint · 2026

An explicit formula for Koornwinder moments and Rains' positivity conjecture

With Younggwang Cho, Donghyun Kim, Jang Soo Kim, Hojoon Lee, and Jing Liu.

arXiv:2606.14241

The Ramanujan Journal · 2025

Combinatorics of orthogonal polynomials on the unit circle

With Jihyeug Jang.

Journal article

Advances in Mathematics · 2024

Refined canonical stable Grothendieck polynomials and their duals, Part 1

With Byung-Hak Hwang, Jihyeug Jang, Jang Soo Kim, and U-Keun Song.

arXiv:2104.04251

AI & Mathematics activities

Recent workshops, collaborative projects, and computational experiments in AI for mathematics.

View activities