Lower and Upper Bounds for Nonzero Littlewood-Richardson Coefficients

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.