On Weary Drivers, Records of Trees, and Parking Functions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866910085911937024 |
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| author | Lillo, Adrián Rosas, Mercedes Trandafir, Stefan |
| author_facet | Lillo, Adrián Rosas, Mercedes Trandafir, Stefan |
| contents | This work builds on the notion of record of rooted trees. We provide an alternative definition of parking functions, derive from it a record-preserving bijection between rooted trees and parking functions, and establish a join equidistribution result between a 5-tuple of statistics on rooted trees and a corresponding 5-tuple of statistics on parking functions. Some enumerative questions are also considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Weary Drivers, Records of Trees, and Parking Functions Lillo, Adrián Rosas, Mercedes Trandafir, Stefan Combinatorics 05A19 (Primary) 05E05, 05A05 (Secondary) This work builds on the notion of record of rooted trees. We provide an alternative definition of parking functions, derive from it a record-preserving bijection between rooted trees and parking functions, and establish a join equidistribution result between a 5-tuple of statistics on rooted trees and a corresponding 5-tuple of statistics on parking functions. Some enumerative questions are also considered. |
| title | On Weary Drivers, Records of Trees, and Parking Functions |
| topic | Combinatorics 05A19 (Primary) 05E05, 05A05 (Secondary) |
| url | https://arxiv.org/abs/2506.22145 |