Séminaire Lotharingien de Combinatoire, 93B.127 (2025), 10 pp.
Emma Yu Jin and Xiaowei Lin
Modified Macdonald Polynomials and μ-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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