Strict unimodality of q-binomial coefficients

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.

4 pages. version 2: minor changes in theorems 1, 6 and lemma 2; details added

References in corpus (3)

• A diagrammatic approach to Kronecker squares
• Kronecker products, characters, partitions, and the tensor square conjectures
• Unimodality via Kronecker products

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• Applications of Gaussian Binomials to Coding Theory for Deletion Error Correction
• A Unified Approach to Unimodality of Gaussian Polynomials