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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.22232 |
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| _version_ | 1866929566955601920 |
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| author | Armon, Sam Beckford, Joanne Hanson, Dillon Krawzik, Naomi Mandelshtam, Olya Martinez, Lucy Yan, Catherine |
| author_facet | Armon, Sam Beckford, Joanne Hanson, Dillon Krawzik, Naomi Mandelshtam, Olya Martinez, Lucy Yan, Catherine |
| contents | Classical parking functions are a generalization of permutations that appear in many combinatorial structures. Prime parking functions are indecomposable components such that any classical parking function can be uniquely described as a direct sum of prime ones. In this article, we extend the notion of primeness to three generalizations of classical parking functions: vector parking functions, $(p,q)$-parking functions, and two-dimensional vector parking functions. We study their enumeration by obtaining explicit formulas for the number of prime vector parking functions when the vector is an arithmetic progression, prime $(p,q)$-parking functions, and prime two-dimensional vector parking functions when the weight matrix is an affine transformation of the coordinates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Primeness of generalized parking functions Armon, Sam Beckford, Joanne Hanson, Dillon Krawzik, Naomi Mandelshtam, Olya Martinez, Lucy Yan, Catherine Combinatorics Classical parking functions are a generalization of permutations that appear in many combinatorial structures. Prime parking functions are indecomposable components such that any classical parking function can be uniquely described as a direct sum of prime ones. In this article, we extend the notion of primeness to three generalizations of classical parking functions: vector parking functions, $(p,q)$-parking functions, and two-dimensional vector parking functions. We study their enumeration by obtaining explicit formulas for the number of prime vector parking functions when the vector is an arithmetic progression, prime $(p,q)$-parking functions, and prime two-dimensional vector parking functions when the weight matrix is an affine transformation of the coordinates. |
| title | Primeness of generalized parking functions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.22232 |