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On Parking Functions and The Tower of Hanoi

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arxiv 2206.00541 v1 pith:257SPS56 submitted 2022-06-01 math.CO

Yasmin Aguillon , Dylan Alvarenga , Pamela E. Harris , Surya Kotapati , J. Carlos Martínez Mori , Casandra D. Monroe , Zia Saylor , Camelle Tieu
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Dwight Anderson Williams II
This is my paper · ORCID
classification math.CO
keywords parkingdisplacementfunctionshanoiparktowerarticlebijection
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abstract

The displacement of a parking function measures the total difference between where cars want to park and where they ultimately park. In this article, we prove that the set of parking functions of length $n$ with displacement one is in bijection with the set of ideal states in the famous Tower of Hanoi game with $n+1$ disks and $n+1$ pegs, both sets being enumerated by the Lah numbers.

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