Symmetry in Tree Parking Distributions
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918132989296640 |
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| author | Getachew, Amanuel T. |
| author_facet | Getachew, Amanuel T. |
| contents | In this paper, we explore parking distributions on caterpillar trees, focusing on two primary statistics: the number of lucky cars and the frequency with which cars prefer specific parking spaces. We use first-return decomposition to reveal a symmetry in their joint distribution and develop a $q, t$-analog of the Fuss-Catalan generating function. We prove that this generating function exhibits specific symmetry and satisfies a functional equation. Additionally, we extend our findings to any m statistics that satisfy certain criteria, presenting a concrete example of such $m$ statistics to illustrate the broader applicability of our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00436 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetry in Tree Parking Distributions Getachew, Amanuel T. Combinatorics In this paper, we explore parking distributions on caterpillar trees, focusing on two primary statistics: the number of lucky cars and the frequency with which cars prefer specific parking spaces. We use first-return decomposition to reveal a symmetry in their joint distribution and develop a $q, t$-analog of the Fuss-Catalan generating function. We prove that this generating function exhibits specific symmetry and satisfies a functional equation. Additionally, we extend our findings to any m statistics that satisfy certain criteria, presenting a concrete example of such $m$ statistics to illustrate the broader applicability of our results. |
| title | Symmetry in Tree Parking Distributions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.00436 |