A sum rule for derangements
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908545426915328 |
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| author | Pain, Jean-Christophe |
| author_facet | Pain, Jean-Christophe |
| contents | We propose a sum rule for derangements. Three different proofs are provided. The first one involves integral representations and the second one relies on the Hermite identity for the integer part of the product of an integer by a real number. The third one, which, unlike the previous ones, is not based on induction, proceeds directly from a recurrence relation for the number of derangements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A sum rule for derangements Pain, Jean-Christophe Number Theory Combinatorics We propose a sum rule for derangements. Three different proofs are provided. The first one involves integral representations and the second one relies on the Hermite identity for the integer part of the product of an integer by a real number. The third one, which, unlike the previous ones, is not based on induction, proceeds directly from a recurrence relation for the number of derangements. |
| title | A sum rule for derangements |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2509.14672 |