# The stability of the Kronecker products of Schur functions

## TL;DR

This paper investigates the stabilization phenomenon of Kronecker products of Schur functions, determining exact stabilization points and improving bounds for the stabilization of Kronecker coefficients.

## Contribution

It precisely computes the stabilization point for Kronecker coefficients and introduces improved bounds, advancing understanding of their asymptotic behavior.

## Key findings

- Exact stabilization value of n for Kronecker products
- Two new bounds for coefficient stabilization
- Improved bounds over previous results by Brion and Vallejo

## 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.