报告题目：The modified Macdonald polynomials and mu-Mahonian statistics

腾讯会议：379-323-490   4月14日 下午15：00-16：00

报告摘要：The modified Macdonald polynomials indexed by partitions are the basis of the symmetric functions in infinitely many variables with coefficients in the field of rational functions of two variables. The combinatorial investigation of modified Macdonald polynomials has been greatly promoted by the celebrated breakthrough on the connections between them and mu-Mahonian statistics on fillings of Young diagrams due to Haglund, Haiman and Loehr (2005).

Recently, Corteel, Haglund, Mandelshtam, Mason and Williams (2021) discovered a compact formula for the modified Macdonald polynomials and made a conjecture on an equivalent form of them. This was subsequently affirmed by Ayyer, Mandelshtam and Martin (2023) and they proposed a stronger conjecture on a refined equivalence. Our main result confirms their conjecture. That is, we establish the equidistribution between the pairs (inv, maj) and (quinv, maj) on any row-equivalency class of a given filling of a Young diagram. In particular if the Young diagram is rectangular, the triples (inv, quinv, maj) and (quinv, inv, maj) have the same distribution over the row-equivalence class. This talk is based on joint work with Xiaowei Lin.

个人简介：靳宇，厦门大学国产自拍 教授，博士生导师。主要研究方向是组合数学。2005年西南大学本科毕业，2010年南开大学组合数学中心博士毕业，之后在德国Kaiserslautern大学，奥地利维也纳科技大学和维也纳大学做博士后研究。2021年回国入职厦门大学。