Bounds on certain classes of Kronecker and q-binomial coefficients

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:147

Article

Pak, Igor¹  Panova, Greta² 

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[2] Univ Penn, Dept Math, Philadelphia, PA 19103 USA

关键词: Kronecker coefficients of the;    symmetric group;    q-binomial coefficients;    Partitions asymptotics;    Irreducible characters;    Alternating group;   

DOI  :  10.1016/j.jcta.2016.10.004

来源: Elsevier

【 摘 要 】

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 ((n)(k)) 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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