On Parking Functions and The Tower of Hanoi
| Autor: | Aguillon, Yasmin, Alvarenga, Dylan, Harris, Pamela E., Kotapati, Surya, Mori, J. Carlos Martínez, Monroe, Casandra D., Saylor, Zia, Tieu, Camelle, Williams II, Dwight Anderson |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1080/00029890.2023.2206311 |
| Popis: | 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. Comment: 7 pages; 4 figures (5 image files); Final version to appear in The American Mathematical Monthly |
| Databáze: | arXiv |
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