Séminaire Lotharingien de Combinatoire, 93B.145 (2025), 12 pp.
Kyle Celano, Jennifer Elder, Kimberly P. Hadaway, Pamela E. Harris, Amanda Priestley and Gabe Udell
Inversions in Parking Functions
Abstract.
In this paper, we obtain a q-exponential generating function for inversions on parking functions in two ways (1) via symmetric function theory and (2) through a direct bijection to labeled rooted forests.
Moreover, we obtain an expression for the total number of inversions across all parking functions via a probabilistic approach.
Finally, by applying these techniques to \textit{unit interval parking functions} (defined by Hadaway 2021) we give analogous results.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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