Some identities involving $q$-Stirling numbers of the second kind in type B
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913192939094016 |
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| author | Ding, Ming-Jian Zeng, Jiang |
| author_facet | Ding, Ming-Jian Zeng, Jiang |
| contents | The recent interest in $q$-Stirling numbers of the second kind in type B prompted us to give a type B analogue of a classical identity connecting the $q$-Stirling numbers of the second kind and Carlitz's major $q$-Eulerian numbers, which turns out to be a $q$-analogue of an identity due to Bagno, Biagioli and Garber. We provide a combinatorial proof of this identity and an analytical proof of a more general identity for colored permutations. In addition, we prove some $q$-identities about the $q$-Stirling numbers of the second kind in types A, B and D. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00570 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some identities involving $q$-Stirling numbers of the second kind in type B Ding, Ming-Jian Zeng, Jiang Combinatorics 05A05, 05A18, 05A19 The recent interest in $q$-Stirling numbers of the second kind in type B prompted us to give a type B analogue of a classical identity connecting the $q$-Stirling numbers of the second kind and Carlitz's major $q$-Eulerian numbers, which turns out to be a $q$-analogue of an identity due to Bagno, Biagioli and Garber. We provide a combinatorial proof of this identity and an analytical proof of a more general identity for colored permutations. In addition, we prove some $q$-identities about the $q$-Stirling numbers of the second kind in types A, B and D. |
| title | Some identities involving $q$-Stirling numbers of the second kind in type B |
| topic | Combinatorics 05A05, 05A18, 05A19 |
| url | https://arxiv.org/abs/2307.00570 |