  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.
