Self-modified difference ascent sequences
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912434395021312 |
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| author | Cerbai, Giulio Claesson, Anders Sagan, Bruce E. |
| author_facet | Cerbai, Giulio Claesson, Anders Sagan, Bruce E. |
| contents | Ascent sequences play a key role in the combinatorics of Fishburn structures. Difference ascent sequences are a natural generalization obtained by replacing ascents with $d$-ascents. We have recently extended the so-called hat map to difference ascent sequences, and self-modified difference ascent sequences are the fixed points under this map. We characterize self-modified difference ascent sequences and enumerate them in terms of certain generalized Fibonacci polynomials. Furthermore, we describe the corresponding subset of $d$-Fishburn permutations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_06959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-modified difference ascent sequences Cerbai, Giulio Claesson, Anders Sagan, Bruce E. Combinatorics 05A19, 05A05 Ascent sequences play a key role in the combinatorics of Fishburn structures. Difference ascent sequences are a natural generalization obtained by replacing ascents with $d$-ascents. We have recently extended the so-called hat map to difference ascent sequences, and self-modified difference ascent sequences are the fixed points under this map. We characterize self-modified difference ascent sequences and enumerate them in terms of certain generalized Fibonacci polynomials. Furthermore, we describe the corresponding subset of $d$-Fishburn permutations. |
| title | Self-modified difference ascent sequences |
| topic | Combinatorics 05A19, 05A05 |
| url | https://arxiv.org/abs/2408.06959 |