  In this paper we give a combinatorial interpretation for the coefficient of
$s_{\nu}$ in the Kronecker product $s_{(n-p,p)}\ast s_{\lambda}$, where
$\lambda=(\lambda_1, ..., \lambda_{\ell(\lambda)})\vdash n$, if
$\ell(\lambda)\geq 2p-1$ or $\lambda_1\geq 2p-1$; that is, if $\lambda$ is not
a partition inside the $2(p-1)\times 2(p-1)$ square. For $\lambda$ inside the
square our combinatorial interpretation provides an upper bound for the
coefficients. In general, we are able to combinatorially compute these
coefficients for all $\lambda$ when $n>(2p-2)^2$. We use this combinatorial
interpretation to give characterizations for multiplicity free Kronecker
products. We have also obtained some formulas for special cases.
