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Strict unimodality of q-binomial coefficients

arXiv:1306.5085 · doi:10.1016/j.crma.2013.06.008

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