Lower and Upper Bounds for Nonzero Littlewood-Richardson Coefficients

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