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arXiv · 2508.11587

Inversions in parking functions

Kyle Celano·Jennifer Elder·Kimberly P. Hadaway·Pamela E. Harris·Amanda Priestley·Gabe Udell
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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.

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Kyle Celano, Jennifer Elder, Kimberly P. Hadaway, Pamela E. Harris, Amanda Priestley, Gabe Udell. 2025-08-15. Inversions in parking functions. https://arxiv.org/abs/2508.11587

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