English

The stability of the Kronecker products of Schur functions

Representation Theory 2020-04-14 v2 Combinatorics

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.

Keywords

Cite

@article{arxiv.0907.4652,
  title  = {The stability of the Kronecker products of Schur functions},
  author = {Emmanuel Briand and Rosa Orellana and Mercedes Rosas},
  journal= {arXiv preprint arXiv:0907.4652},
  year   = {2020}
}

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16 pages