Stability of coefficients in the Kronecker product of a hook and a rectangle

2014/12/03 by Cristina Ballantine, Ballantine, Cristina, Bill Hallahan +1
Mathematics · #Advanced Combinatorial Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1412.1431

13 pages

arxiv created 2014/12/03 · arxiv updated 2014/12/04

Abstract

We use recent work of Jonah Blasiak (2012) to prove a stability result for the coefficients in the Kronecker product of two Schur functions: one indexed by a hook partition and one indexed by a rectangle partition. We also give bounds for the size of the partition starting with which the Kronecker coefficients are stable. Moreover, we show that once the bound is reached, no new Schur functions appear in the decomposition of Kronecker product, thus allowing one to recover the decomposition from the smallest case in which the stability holds.

Related

• The stability of the Kronecker products of Schur functions
• The Kronecker product of Schur functions indexed by two-row shapes or hook shapes
• Stability of the Heisenberg Product on Symmetric Functions
• On rectangular Kronecker coefficients
• The partition algebra and the Kronecker coefficients