An involution for a Catalan-tangent number identity
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917108438269952 |
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| author | Kim, Dongsu Lin, Zhicong |
| author_facet | Kim, Dongsu Lin, Zhicong |
| contents | We provide an involution proof of a Catalan-tangent number identity arising from the study of peak algebra that was found by Aliniaeifard and Li. In the course, we find a new combinatorial identity for the tangent numbers $T_{2n+1}$: $$ \sum_{k=0}^{n}(-1)^{k}{2n+1\choose 2k}2^{2n-2k}T_{2k+1}=(-1)^nT_{2n+1}. $$ Moreover, we derive two different $q$-analogs of the above identity from the combinatorial perspective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An involution for a Catalan-tangent number identity Kim, Dongsu Lin, Zhicong Combinatorics We provide an involution proof of a Catalan-tangent number identity arising from the study of peak algebra that was found by Aliniaeifard and Li. In the course, we find a new combinatorial identity for the tangent numbers $T_{2n+1}$: $$ \sum_{k=0}^{n}(-1)^{k}{2n+1\choose 2k}2^{2n-2k}T_{2k+1}=(-1)^nT_{2n+1}. $$ Moreover, we derive two different $q$-analogs of the above identity from the combinatorial perspective. |
| title | An involution for a Catalan-tangent number identity |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.22157 |