A Colorful Way to Park: An Introduction to Exact $k$-Typed Parking Functions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911475572932608 |
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| author | Celestine, Aalliyah van der Leeuw, Jacob Liu, Lina |
| author_facet | Celestine, Aalliyah van der Leeuw, Jacob Liu, Lina |
| contents | Parking functions are tuples that describe the parking of $M$ cars on a street with $M$ parking spots. In this paper, we define exact $k$-typed parking functions ($k$-TPFs) to be a variant of classical parking functions. We then establish that every exact $k$-TPF $α$ of length $M$, corresponds to a unique parking configuration $C$. We observe that the collection of all exact $k$-TPFs which result in the same configuration form a disjoint subset of all exact $k$-TPFs. Lastly, we conclude by showing how parking permutations of an exact $k$-TPF can be related to other combinatorial objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00826 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Colorful Way to Park: An Introduction to Exact $k$-Typed Parking Functions Celestine, Aalliyah van der Leeuw, Jacob Liu, Lina Combinatorics 05A99 Parking functions are tuples that describe the parking of $M$ cars on a street with $M$ parking spots. In this paper, we define exact $k$-typed parking functions ($k$-TPFs) to be a variant of classical parking functions. We then establish that every exact $k$-TPF $α$ of length $M$, corresponds to a unique parking configuration $C$. We observe that the collection of all exact $k$-TPFs which result in the same configuration form a disjoint subset of all exact $k$-TPFs. Lastly, we conclude by showing how parking permutations of an exact $k$-TPF can be related to other combinatorial objects. |
| title | A Colorful Way to Park: An Introduction to Exact $k$-Typed Parking Functions |
| topic | Combinatorics 05A99 |
| url | https://arxiv.org/abs/2603.00826 |