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Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings (1805.00992v2)
Published 2 May 2018 in math.CO
Abstract: We prove and generalize a conjecture in arXiv:1610.0474(4) about the asymptotics of $\frac{1}{\sqrt{n!}} f{\lambda/\mu}$, where $f{\lambda/\mu}$ is the number of standard Young tableaux of skew shape $\lambda/\mu$ which have stable limit shape under the $1/\sqrt{n}$ scaling. The proof is based on the variational principle on the partition function of certain weighted lozenge tilings.
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