Explicit estimates for the Stirling numbers of the second kind
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914866400329728 |
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| author | Adell, José A. |
| author_facet | Adell, José A. |
| contents | We give explicit estimates for the Stirling numbers of the second kind $S(n,m)$. With a few exceptions, such estimates are asymptotically sharp. The form of these estimates varies according to $m$ lying in the central or non-central regions of $\{1,\ldots ,n\}$. In each case, we use a different probabilistic representation of $S(n,m)$ in terms of well known random variables to show the corresponding results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08246 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit estimates for the Stirling numbers of the second kind Adell, José A. Combinatorics 05A18, 60E05 We give explicit estimates for the Stirling numbers of the second kind $S(n,m)$. With a few exceptions, such estimates are asymptotically sharp. The form of these estimates varies according to $m$ lying in the central or non-central regions of $\{1,\ldots ,n\}$. In each case, we use a different probabilistic representation of $S(n,m)$ in terms of well known random variables to show the corresponding results. |
| title | Explicit estimates for the Stirling numbers of the second kind |
| topic | Combinatorics 05A18, 60E05 |
| url | https://arxiv.org/abs/2407.08246 |