Polynomiality of certain average weights for oscillating tableaux

TL;DR

This paper proves that certain average weights for oscillating tableaux are polynomial functions of their length and ending partition size, extending previous results and providing explicit and asymptotic formulas.

Contribution

It generalizes prior work by showing polynomiality of average weights in two variables and derives explicit and asymptotic formulas.

Findings

Average weights are polynomials in length and ending partition size.

Derived explicit formulas for average weights.

Provided asymptotic behavior of these weights.

Abstract

We prove that a family of average weights for oscillating tableaux are polynomials in two variables, namely, the length of the oscillating tableau and the size of the ending partition, which generalizes a result of Hopkins and Zhang. Several explicit and asymptotic formulas for the average weights are also derived.