Enumerating Pattern Avoiding Parking Functions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916040825372672 |
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| author | Adenbaum, Ben |
| author_facet | Adenbaum, Ben |
| contents | In this paper, we complete the enumeration of the number of parking functions of length $n$ avoiding, in the sense defined by Qiu and Remmel, a permutation of length 3, answering several questions of Adeniran and Pudwell. Additionally, we provide explicit growth rates for the number of parking functions of length $n$ avoiding a monotonic pattern of any length. As a consequence of our techniques we additionally provide a combinatorial enumeration for the number of equivalence classes of words with a fixed content under the Sylvester congruence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24092 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Enumerating Pattern Avoiding Parking Functions Adenbaum, Ben Combinatorics In this paper, we complete the enumeration of the number of parking functions of length $n$ avoiding, in the sense defined by Qiu and Remmel, a permutation of length 3, answering several questions of Adeniran and Pudwell. Additionally, we provide explicit growth rates for the number of parking functions of length $n$ avoiding a monotonic pattern of any length. As a consequence of our techniques we additionally provide a combinatorial enumeration for the number of equivalence classes of words with a fixed content under the Sylvester congruence. |
| title | Enumerating Pattern Avoiding Parking Functions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.24092 |