Synchronicity of descent and excedance enumerators in the alternating subgroup
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917628894773248 |
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| author | Shankar, Umesh |
| author_facet | Shankar, Umesh |
| contents | Generalising the work of Dey, we define the notion of ultra-synchronicity of sequences of real numbers. Let $B_{n,k},C_{n,k},P_{n,k},Q_{n,k}$ be the number of even permutations with $k$ descents, odd permutations with $k$ descents, even permutations with $k$ excedances and odd permutations with $k$ excedances respectively. We show that the four sequences are ultra-synchronised for all $n\ge 5$. This proves a strengthening of two conjectures of Dey. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Synchronicity of descent and excedance enumerators in the alternating subgroup Shankar, Umesh Combinatorics 05A05, 05A20 Generalising the work of Dey, we define the notion of ultra-synchronicity of sequences of real numbers. Let $B_{n,k},C_{n,k},P_{n,k},Q_{n,k}$ be the number of even permutations with $k$ descents, odd permutations with $k$ descents, even permutations with $k$ excedances and odd permutations with $k$ excedances respectively. We show that the four sequences are ultra-synchronised for all $n\ge 5$. This proves a strengthening of two conjectures of Dey. |
| title | Synchronicity of descent and excedance enumerators in the alternating subgroup |
| topic | Combinatorics 05A05, 05A20 |
| url | https://arxiv.org/abs/2404.01783 |