Kronecker products and the RSK correspondence
Abstract
The starting point for this work is an identity that relates the number of minimal matrices with prescribed 1-marginals and coefficient sequence to a linear combination of Kronecker coefficients. In this paper we provide a bijection that realizes combinatorially this identity. As a consequence we obtain an algorithm that to each minimal matrix associates a minimal component, with respect to the dominance order, in a Kronecker product, and a combinatorial description of the corresponding Kronecker coefficient in terms of minimal matrices and tableau insertion. Our bijection follows from a generalization of the dual RSK correspondence to 3-dimensional binary matrices, which we state and prove. With the same tools we also obtain a generalization of the RSK correspondence to 3-dimensional integer matrices.
Cite
@article{arxiv.1003.4482,
title = {Kronecker products and the RSK correspondence},
author = {Diana Avella-Alaminos and Ernesto Vallejo},
journal= {arXiv preprint arXiv:1003.4482},
year = {2014}
}