Please join the Department of Mathematics and Statistics on Wednesday, November 3rd at 3:30pm in Innovation E100 for a fascinating REU combinatorics seminar featuring our very own, Mazie O’Connor.

Skeletal Parking Functions

Mazie O’Connor, University of Vermont

Wednesday, November 3rd, 3:30PM, Innovation E100

Abstract: Parking functions of order n are classical combinatorial objects which arise in different areas of mathematics.  Using the theory of chip-firing on graphs with respect to a simplicial complex, I will introduce for each positive integer k at most n, a family of generalizations of parking functions called k-skeletal parking functions.  Skeletal parking functions retain two desirable properties:  1) they have the same cardinality as classical parking functions and 2) they have an S_n action which is isomorphic to the standard action of S_n on parking functions.  I will give an overview of our construction and explain how it leads to a new generalization of Dyck paths.  This is joint work with Spencer Backman, Cole Charbonneau, Patrick Mullins, and Greg Warrington.