Algebra and Combinatorics Seminar

Date: December 5, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Yeong-Nan Yeh, Institute of Mathematics, Academia Sinica

Title: γ-Minimal parking functions and permutation statistics

Abstract: In this talk, given a choice function γ, we will introduce the concept of γ-minimal parking functions, discuss properties of γ-minimal parking functions and study some permutation statistics from the point of view of γ-minimal parking functions. In particular, for some choice functions γ, we will characterize γ-minimal parking functions. We will also discuss a family of bijections from the set of γ-minimal parking functions of length n to the set of permutations of {1, 2,…, n}. We define some permutation statistics via γ-minimal parking functions, derive the recurrent relations of the generating functions for these statistics and show that several statistics are Mahonian.