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arXiv · 0907.4652

The stability of the Kronecker products of Schur functions

Emmanuel Briand·Rosa Orellana·Mercedes Rosas
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Abstract

In the late 1930's Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n sufficiently large, the values of the Kronecker coefficients appearing in the product of two Schur functions of degree n do not depend on the first part of the indexing partitions, but only on the values of their remaining parts. We compute the exact value of n for which all the coefficients of a Kronecker product of Schur functions stabilize. We also compute two new bounds for the stabilization of a sequence of coefficients and show that they improve existing bounds of M. Brion and E. Vallejo.

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Emmanuel Briand, Rosa Orellana, Mercedes Rosas. 2009-08-06. The stability of the Kronecker products of Schur functions. https://doi.org/10.1016/j.jalgebra.2010.12.026

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