On Parking Functions and The Tower of Hanoi
Combinatorics
2023-12-13 v1
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 with displacement one is in bijection with the set of ideal states in the famous Tower of Hanoi game with disks and pegs, both sets being enumerated by the Lah numbers.
Cite
@article{arxiv.2206.00541,
title = {On Parking Functions and The Tower of Hanoi},
author = {Yasmin Aguillon and Dylan Alvarenga and Pamela E. Harris and Surya Kotapati and J. Carlos Martínez Mori and Casandra D. Monroe and Zia Saylor and Camelle Tieu and Dwight Anderson Williams},
journal= {arXiv preprint arXiv:2206.00541},
year = {2023}
}
Comments
7 pages; 4 figures (5 image files); Final version to appear in The American Mathematical Monthly