Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Celano, Kyle, Elder, Jennifer, Hadaway, Kimberly P., Harris, Pamela E., Priestley, Amanda, Udell, Gabe
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7075993865
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