2022 Combinatorics Workshop

$(q,t)$-analogues of $n!$ and $(n+1)^{n-1}$

1 Oct 2022, 15:15

20m

Contributed talk Session 4

Speaker

Jaeseong Oh (Korea Institute for Advanced Study)

Description

The numbers $n!$ and $(n+1)^{n-1}$ are ubiquitous in combinatorics. Each number counts number of permutations and parking functions, respectively. I will discuss their $(q,t)$-generalizations and further generalization to symmetric functions, namely the modified Macdonald polynomials $\widetilde{H}_\mu$ and $\nabla e_n$. Then I will discuss a recent conjecture involving these two symmetric functions. Based on joint work with Donghyun Kim and Seung Jin Lee.