Lower and Upper Bounds for Nonzero Littlewood-Richardson Coefficients

Abstract

Given a skew diagram $\gamma/\lambda$, we determine a set of lower and upper bounds that a partition $\mu$ must satisfy for Littlewood-Richards coefficients $c^{\gamma}_{\lambda,\mu}>0$. Our algorithm depends on the characterization of $c^{\gamma}_{\lambda,\mu}$ as the number of Littlewood-Richardson tableau of shape $\gamma/\lambda$ and content $\mu$ and uses the (generalized) dominance order on partitions as the main ingredient.