Speaker: 靳宇，厦门大学

Title: Modified Macdonald polynomials and Mahonian statistics

Language: Chinese

Time & Venue: 2024.08.15 10:15-11:15 思源楼525

Abstract: We establish an equidistribution between the pairs (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 (2021) and a conjecture by Corteel, Haglund, Mandelshtam, Mason and Williams (2019), thus presenting the equivalence between two refined formulas for the modified Macdonald polynomials. This is joint work with Xiaowei Lin.