Type-B analogue of Bell numbers using Rota's Umbral calculus approach
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916298771922944 |
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| author | Bagno, Eli Garber, David |
| author_facet | Bagno, Eli Garber, David |
| contents | Rota used the functional L to recover old properties and obtain some new formulas for the Bell numbers. Tanny used Rota's functional L and the celebrated Worpitzky identity to obtain some expression for the ordered Bell numbers, which can be seen as an evident to the fact that the ordered Bell numbers are gamma-positive. In this paper, we extend some of Rota's and Tanny's results to the framework of the set partitions of Coxeter type B. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Type-B analogue of Bell numbers using Rota's Umbral calculus approach Bagno, Eli Garber, David Discrete Mathematics Combinatorics Rota used the functional L to recover old properties and obtain some new formulas for the Bell numbers. Tanny used Rota's functional L and the celebrated Worpitzky identity to obtain some expression for the ordered Bell numbers, which can be seen as an evident to the fact that the ordered Bell numbers are gamma-positive. In this paper, we extend some of Rota's and Tanny's results to the framework of the set partitions of Coxeter type B. |
| title | Type-B analogue of Bell numbers using Rota's Umbral calculus approach |
| topic | Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2406.16393 |