Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings

2018/05/02 by Morales, Alejandro, Pak, Igor, Tassy, Martin · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.00992

Abstract

We prove and generalize a conjecture in arXiv:1610.0474(4) about the asymptotics of (1)/(√(n!)) f^λ/μ, where f^λ/μ is the number of standard Young tableaux of skew shape λ/μ which have stable limit shape under the 1/√(n) scaling. The proof is based on the variational principle on the partition function of certain weighted lozenge tilings.

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