Asymptotics for skew standard Young tableaux via bounds for characters

2017/10/16 by Dousse, Jehanne, Féray, Valentin · 2 citations
#05A16 #05E05 #05E10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.05652

Abstract

We are interested in the asymptotics of the number of standard Young tableaux f^λ/μ of a given skew shape λ/μ. We mainly restrict ourselves to the case where both diagrams are balanced, but investigate all growth regimes of |μ| compared to |λ|, from |μ| fixed to |μ| of order |λ|. When |μ|=o(|λ|^1/3), we get an asymptotic expansion to any order. When |μ|=o(|λ|^1/2), we get a sharp upper bound. For bigger |μ|, we prove a weaker bound and give a conjecture on what we believe to be the correct order of magnitude. Our results are obtained by expressing f^λ/μ in terms of irreducible character values of the symmetric group and applying known upper bounds on characters.

Cited by

• Asymptotics of higher Lie characters
• Bounds on skew dimensions and characters of symmetric groups via thick hook decompositions

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