Counting Orbits of Defective Parking Functions

Alex Moon
PhD Student
University of Wisconsin-Milwaukee

Parking functions are well-studied objects in combinatorics and representation theory which constitute tuples of preferred parking spots for cars under a linear parking scheme. This talk will generalize to defective parking functions. I will enumerate the orbits of defective parking functions under the action of the symmetric group by characterizing them as nondecreasing tuples and sketching a bijection to standard nondecreasing parking functions. I will also introduce the concept of the conjugate of a nondecreasing parking function in order to simplify the case where the number of cars and spots differ.

This is a joint with Pamela E. Harris, Aaron Ortiz, Lauren J. Quesada, Cynthia Marie Rivera Sánchez, and Dwight A. Williams II.