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arXiv · 1003.4482

Kronecker products and the RSK correspondence

Diana Avella-Alaminos·Ernesto Vallejo
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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.

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Diana Avella-Alaminos, Ernesto Vallejo. 2010-03-23. Kronecker products and the RSK correspondence. https://doi.org/10.1016/j.disc.2012.01.006

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