报告时间：2024年4月20日（星期六）9：30-

报告地点：腾讯会议，ID：379-273-574

报告人：Amarpreet Rattan副教授

工作单位：SimonFraser University,加拿大

举办单位：英国威廉希尔公司

报告简介：

For fixed n, consider the symmetric group S_n on the symbols 1,...,n and the set of *star* transpositions, the transpositions that contain the symbol n. A *star factorization* of a permutation b in S_n of length k is the writing of b as the product of k star transpositions. Goulden and Jackson (2009) showed that the number of such factorizations only depends on the conjugacy class of b and not on b itself, a remarkable fact given the special role the symbol n plays amongst star transpositions. We supply the first fully combinatorial proof of this fact that works for all lengths k, and our methods connect star factorizations to monotone factorizations. Star transpositions are connected to Jucys-Murphy elements, and we explain how our result can give expressions for the *transitive* image of certain symmetric functions evaluated at Jucys-Murphy elements.

报告人简介：

Amarpreet Rattan is an Associate Professor of Mathematics at Simon Fraser University in Canada. He did his PhD at the University of Waterloo under the supervision of Ian Goulden. His primary research area is algebraic combinatorics.