Pattern avoidance in revised ascent sequences
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915278060781568 |
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| author | Zhou, Robin D. P. |
| author_facet | Zhou, Robin D. P. |
| contents | Inspired by the definition of modified ascent sequences, we introduce a new class of integer sequences called revised ascent sequences. These sequences are defined as Cayley permutations where each entry is a leftmost occurrence if and only if it serves as an ascent bottom. We construct a bijection between ascent sequences and revised ascent sequences by adapting the classic hat map, which transforms ascent sequences into modified ascent sequences. Additionally, we investigate revised ascent sequences that avoid a single pattern, leading to a wealth of enumerative results. Our main techniques include the use of bijections, generating trees, generating functions, and the kernel method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_05171 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pattern avoidance in revised ascent sequences Zhou, Robin D. P. Combinatorics Inspired by the definition of modified ascent sequences, we introduce a new class of integer sequences called revised ascent sequences. These sequences are defined as Cayley permutations where each entry is a leftmost occurrence if and only if it serves as an ascent bottom. We construct a bijection between ascent sequences and revised ascent sequences by adapting the classic hat map, which transforms ascent sequences into modified ascent sequences. Additionally, we investigate revised ascent sequences that avoid a single pattern, leading to a wealth of enumerative results. Our main techniques include the use of bijections, generating trees, generating functions, and the kernel method. |
| title | Pattern avoidance in revised ascent sequences |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.05171 |