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-Richar...
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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.2208.06541 |