Kronecker products and the RSK correspondence.

DOI10.1016/J.DISC.2012.01.006zbMATH Open1257.20008arXiv1003.4482OpenAlexW2048226952MaRDI QIDQ408189

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Publication date: 29 March 2012

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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.

Full work available at URL: https://arxiv.org/abs/1003.4482

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