Odd-indexed Fibonacci numbers via pattern-avoiding permutations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917355794202624 |
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| author | Gil, Juan B. Xu, Felix H. Zhu, William Y. |
| author_facet | Gil, Juan B. Xu, Felix H. Zhu, William Y. |
| contents | In this paper, we consider several combinatorial problems whose enumeration leads to the odd-indexed Fibonacci numbers, including certain types of Dyck paths, block fountains, directed column-convex polyominoes, and set partitions with no crossings and no nestings. Our goal is to provide bijective maps to pattern-avoiding permutations and derive generating functions that track certain positional statistics at the permutation level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Odd-indexed Fibonacci numbers via pattern-avoiding permutations Gil, Juan B. Xu, Felix H. Zhu, William Y. Combinatorics 05A19 (Primary) 05A05, 05A15 (Secondary) In this paper, we consider several combinatorial problems whose enumeration leads to the odd-indexed Fibonacci numbers, including certain types of Dyck paths, block fountains, directed column-convex polyominoes, and set partitions with no crossings and no nestings. Our goal is to provide bijective maps to pattern-avoiding permutations and derive generating functions that track certain positional statistics at the permutation level. |
| title | Odd-indexed Fibonacci numbers via pattern-avoiding permutations |
| topic | Combinatorics 05A19 (Primary) 05A05, 05A15 (Secondary) |
| url | https://arxiv.org/abs/2506.15800 |