Asymptotics of the number of standard Young tableaux of skew shape

TL;DR

This paper provides new bounds and asymptotic estimates for counting standard Young tableaux of skew shapes, utilizing Naruse's hook-length formula, and compares these bounds with existing bounds on linear extensions of related posets.

Contribution

It introduces novel bounds and asymptotic estimates for skew shape tableaux counts using Naruse's hook-length formula, enhancing understanding of their asymptotic behavior.

Findings

New bounds for skew shape tableaux counts

Asymptotic estimates derived for special cases

Comparison with existing bounds on linear extensions

Abstract

We give new bounds and asymptotic estimates on the number of standard Young tableaux of skew shape in a variety of special cases. Our approach is based on Naruse's hook-length formula. We also compare our bounds with the existing bounds on the numbers of linear extensions of the corresponding posets.