On Bell numbers of type $D$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910917245009920 |
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| author | Arslan, Hasan Alemdar, Nazmiye Zaarour, Mariam Altındiş, Hüseyin |
| author_facet | Arslan, Hasan Alemdar, Nazmiye Zaarour, Mariam Altındiş, Hüseyin |
| contents | In this paper, we will introduce Bell numbers $D(n)$ of type $D$ as an analogue to the classical Bell numbers related to all the partitions of the set $[n]$. Then based on a signed set partition of type $D$, we will construct the recurrence relations of Bell numbers $D(n)$. In addition, we deduce the exponential generating function for $D(n)$. Finally, we will provide an explicit formula for $D(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16522 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Bell numbers of type $D$ Arslan, Hasan Alemdar, Nazmiye Zaarour, Mariam Altındiş, Hüseyin Combinatorics 05A05, 05A15, 05A18, 05A19, 11B73 In this paper, we will introduce Bell numbers $D(n)$ of type $D$ as an analogue to the classical Bell numbers related to all the partitions of the set $[n]$. Then based on a signed set partition of type $D$, we will construct the recurrence relations of Bell numbers $D(n)$. In addition, we deduce the exponential generating function for $D(n)$. Finally, we will provide an explicit formula for $D(n)$. |
| title | On Bell numbers of type $D$ |
| topic | Combinatorics 05A05, 05A15, 05A18, 05A19, 11B73 |
| url | https://arxiv.org/abs/2504.16522 |