Séminaire Lotharingien de Combinatoire, 93B.127 (2025), 10 pp.
Emma Yu Jin and Xiaowei Lin
Modified Macdonald Polynomials and Mahonian Statistics
Abstract.
We establish an equidistribution between the pairs of statistics
(inv,maj) and
(quinv,maj) on any row-equivalency class [τ] where τ is a filling of a given Young diagram. In particular if τ is a filling of a rectangular diagram, the triples (inv,quinv,maj) and (quinv,inv,maj) have the same distribution over [τ].
Our main result affirms a conjecture proposed by Ayyer, Mandelshtam and Martin, thus presenting the equivalence between two refined formulas for the modified Macdonald polynomials.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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