  In this paper we give a new sufficient condition for a general stability of
Kronecker coefficients, which we call it additive stability. It was motivated
by a recent talk of J. Stembridge at the conference in honor of Richard P.
Stanley's 70th birthday, and it is based on work of the author on discrete
tomography along the years. The main contribution of this paper is the
discovery of the connection between additivity of integer matrices and
stability of Kronecker coefficients. Additivity, in our context, is a concept
from discrete tomography. Its advantage is that it is very easy to produce lots
of examples of additive matrices and therefore of new instances of stability
properties. We also show that Stembridge's hypothesis and additivity are
closely related, and prove that all stability properties of Kronecker
coefficients discovered before fit into additive stability.
