Modified Macdonald polynomials and Mahonian statistics

Emma Yu Jin, Xiaowei Lin

Published 2024-07-19Version 1

We establish an equidistribution between the pairs (inv,maj) and (quinv,maj) on any row-equivalency class $[\tau]$ where $\tau$ is a filling of a given Young diagram. In particular if $\tau$ is a filling of a rectangular diagram, the triples (inv,quinv,maj) and (quinv,inv,maj) have the same distribution over $[\tau]$. Our main result affirms a conjecture proposed by Ayyer, Mandelshtam and Martin (2021), thus presenting the equivalence between two refined formulas for the modified Macdonald polynomials.