Inversions in parking functions
Combinatorics
2025-08-18 v1
Abstract
In this paper, we obtain a q-exponential generating function for inversions on parking functions via symmetric function theory and also through a direct bijection to rooted labeled forests. We then apply these techniques to unit interval parking functions to give analogous results. We conclude by introducing a probabilistic approach through which we obtain formulas for the total number of inversions and several other statistics across all parking functions and other sets of words closed under rearrangement.
Cite
@article{arxiv.2508.11587,
title = {Inversions in parking functions},
author = {Kyle Celano and Jennifer Elder and Kimberly P. Hadaway and Pamela E. Harris and Amanda Priestley and Gabe Udell},
journal= {arXiv preprint arXiv:2508.11587},
year = {2025}
}
Comments
30 pages, 3 figures