Strict unimodality of q-binomial coefficients

TL;DR

This paper proves that q-binomial coefficients are strictly unimodal polynomials in q, using combinatorial Young tableaux and properties of Kronecker coefficients of symmetric group representations.

Contribution

It introduces a novel proof of strict unimodality for q-binomial coefficients leveraging combinatorics and representation theory.

Findings

q-binomial coefficients are strictly unimodal in q

The proof utilizes Young tableaux combinatorics

Semigroup property of Kronecker coefficients is key

Abstract

We prove strict unimodality of the q-binomial coefficients \binom{n}{k}_q as polynomials in q. The proof is based on the combinatorics of certain Young tableaux and the semigroup property of Kronecker coefficients of S_n representations.