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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.08426 |
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| _version_ | 1866916869898764288 |
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| author | Cerbai, Giulio Claesson, Anders |
| author_facet | Cerbai, Giulio Claesson, Anders |
| contents | Eulerian polynomials record the distribution of descents over permutations. Caylerian polynomials likewise record the distribution of descents over Cayley permutations, where a Cayley permutation is a word of positive integers such that if a number appears in the word then all positive integers less than that number also appear in the word. Using combinatorial species and sign-reversing involutions we derive counting formulas and generating functions for the Caylerian polynomials as well as for related refined polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08426 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enumerative aspects of Caylerian polynomials Cerbai, Giulio Claesson, Anders Combinatorics Eulerian polynomials record the distribution of descents over permutations. Caylerian polynomials likewise record the distribution of descents over Cayley permutations, where a Cayley permutation is a word of positive integers such that if a number appears in the word then all positive integers less than that number also appear in the word. Using combinatorial species and sign-reversing involutions we derive counting formulas and generating functions for the Caylerian polynomials as well as for related refined polynomials. |
| title | Enumerative aspects of Caylerian polynomials |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.08426 |