Bounds on Kronecker and $q$-binomial coefficients

Igor Pak, Greta Panova

Published 2014-10-26Version 1

We present a lower bound on the Kronecker coefficients 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