Bounds on the Kronecker coefficients

2014/06/11 by Pak, Igor, Panova, Greta
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1406.2988

Abstract

We present several upper and lower bounds on the Kronecker coefficients of the symmetric group. We prove k-stability of the Kronecker coefficients generalizing the (usual) stability, and giving a new upper bound. We prove a lower bound via the characters of S_n. We apply these and other results to generalize Sylvester's unimodality of the q-binomial coefficients \binomnk_q as polynomials in q: we derive explicit sharp bounds on the differences of their consecutive coefficients.

Related

• Bounds on Kronecker and q-binomial coefficients
• Unimodality via Kronecker products
• Durfee squares, symmetric partitions and bounds on Kronecker coefficients
• Kronecker Comultiplication of Stable Characters and Restriction From\n S_mn to S_m \× S_n
• The problem of deciding the positivity of Kronecker coefficients and Saxl conjecture