Combinatorics of higher order degenerate r-deranged bell numbers with singletons
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914545863229440 |
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| author | Nkonkobe, Sithembele |
| author_facet | Nkonkobe, Sithembele |
| contents | When one inserts a number of identical bars in between blocks of an ordered set partition, they get a barred preferential arrangement. In this study we define a new generalization of barred preferential arrangements, by considering barred preferential arrangements with no fixed blocks, and ones where the first r elements of a set are singletons. We derive several combinatorial identities. Combinatorially these numbers are a kind of generalized barred preferential arrangements. We also provide some asymptotic results for these numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08304 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Combinatorics of higher order degenerate r-deranged bell numbers with singletons Nkonkobe, Sithembele General Mathematics When one inserts a number of identical bars in between blocks of an ordered set partition, they get a barred preferential arrangement. In this study we define a new generalization of barred preferential arrangements, by considering barred preferential arrangements with no fixed blocks, and ones where the first r elements of a set are singletons. We derive several combinatorial identities. Combinatorially these numbers are a kind of generalized barred preferential arrangements. We also provide some asymptotic results for these numbers. |
| title | Combinatorics of higher order degenerate r-deranged bell numbers with singletons |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2605.08304 |