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arXiv · 1410.7087

Bounds on Kronecker and $q$-binomial coefficients

Igor Pak·Greta Panova
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Abstract

We present a lower bound on the Kronecker coefficients for tensor squares of the symmetric group via the characters of~$S_n$, which we apply to obtain various explicit estimates. Notably, we extend Sylvester's unimodality of $q$-binomial coefficients $\binom{n}{k}_q$ as polynomials in~$q$ to derive sharp bounds on the differences of their consecutive coefficients. We then derive effective asymptotic lower bounds for a wider class of Kronecker coefficients.

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Igor Pak, Greta Panova. 2016-05-02. Bounds on Kronecker and $q$-binomial coefficients. https://arxiv.org/abs/1410.7087

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