Consecutive and quasi-consecutive patterns: $\mathrm{des}$-Wilf classifications and generating functions
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917923044458496 |
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| author | Wang, Yan Fang, Qi Fu, Shishuo Kitaev, Sergey Li, Haijun |
| author_facet | Wang, Yan Fang, Qi Fu, Shishuo Kitaev, Sergey Li, Haijun |
| contents | Motivated by a correlation between the distribution of descents over permutations that avoid a consecutive pattern and those avoiding the respective quasi-consecutive pattern, as established in this paper, we obtain a complete $\des$-Wilf classification for quasi-consecutive patterns of length up to 4. For equivalence classes containing more than one pattern, we construct various descent-preserving bijections to establish the equivalences, which lead to the provision of proper versions of two incomplete bijective arguments previously published in the literature. Additionally, for two singleton classes, we derive explicit bivariate generating functions using the generalized run theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10128 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Consecutive and quasi-consecutive patterns: $\mathrm{des}$-Wilf classifications and generating functions Wang, Yan Fang, Qi Fu, Shishuo Kitaev, Sergey Li, Haijun Combinatorics Discrete Mathematics 05A05, 05A15, 05A19 Motivated by a correlation between the distribution of descents over permutations that avoid a consecutive pattern and those avoiding the respective quasi-consecutive pattern, as established in this paper, we obtain a complete $\des$-Wilf classification for quasi-consecutive patterns of length up to 4. For equivalence classes containing more than one pattern, we construct various descent-preserving bijections to establish the equivalences, which lead to the provision of proper versions of two incomplete bijective arguments previously published in the literature. Additionally, for two singleton classes, we derive explicit bivariate generating functions using the generalized run theorem. |
| title | Consecutive and quasi-consecutive patterns: $\mathrm{des}$-Wilf classifications and generating functions |
| topic | Combinatorics Discrete Mathematics 05A05, 05A15, 05A19 |
| url | https://arxiv.org/abs/2502.10128 |