A probabilistic approach for enumeration of certain Young tableaux

TL;DR

This paper introduces a probabilistic order statistics model for enumerating Young tableaux, providing new proofs and formulas for various types including truncated shapes and tableaux with holes.

Contribution

It develops a novel probabilistic framework for Young tableaux enumeration and derives new product formulas for special shapes and configurations.

Findings

Established an order statistics model for Young tableaux

Provided brief proofs of Frobenius-Young and Aitken formulas

Derived product formulas for truncated and hole-containing tableaux

Abstract

In this paper we establish an order statistics model of Young tableaux. Multiple integration over nested simplexes is applied to the enumeration of Young tableaux. A brief proof of Frobenius-Young's and Aitken's formulas is given. Partially standard Young tableaux and special truncated shapes including tableaux with a hole are discussed, the associated product formulas are given.