  The Kronecker coefficients are the structure constants for the restriction of
irreducible representations of the general linear group $GL(n m)$ into
irreducibles for the subgroup $GL(n)\times GL(m)$. In this work we study the
quasipolynomial nature of the Kronecker function using elementary tools from
polyhedral geometry. We write the Kronecker function in terms of coefficients
of a vector partition function. This allows us to define a new family of
coefficients, the atomic Kronecker coefficients. Our derivation is explicit and
self-contained, and gives a new exact formula and an upper bound for the
Kronecker coefficients in the first nontrivial case.
