Unimodality via Kronecker products
Combinatorics
2014-03-13 v2
Abstract
We present new proofs and generalizations of unimodality of the q-binomial coefficients \binom{n}{k}_q as polynomials in q. We use an algebraic approach by interpreting the differences between numbers of certain partitions as Kronecker coefficients of representations of S_n. Other applications of this approach include strict unimodality of the diagonal q-binomial coefficients and unimodality of certain partition statistics.
Cite
@article{arxiv.1304.5044,
title = {Unimodality via Kronecker products},
author = {Igor Pak and Greta Panova},
journal= {arXiv preprint arXiv:1304.5044},
year = {2014}
}
Comments
to appear in Journal of Algebraic Combinatorics; v2 vs v1 -- added references, incorporated referee's comments