Bounds on Kronecker and $q$-binomial coefficients
Combinatorics
2016-05-04 v3 Representation Theory
Abstract
We present a lower bound on the Kronecker coefficients for tensor squares of the symmetric group via the characters of~, which we apply to obtain various explicit estimates. Notably, we extend Sylvester's unimodality of -binomial coefficients as polynomials in~ 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.
Keywords
Cite
@article{arxiv.1410.7087,
title = {Bounds on Kronecker and $q$-binomial coefficients},
author = {Igor Pak and Greta Panova},
journal= {arXiv preprint arXiv:1410.7087},
year = {2016}
}
Comments
version May 2016: improved the effective constants. To appear in JCTA. This paper is an extension of parts of the earlier paper "Bounds on the Kronecker coefficients" arXiv:1406.2988, which also contains stability results