A sum rule for $r$-derangements obtained from the Cauchy product of exponential generating functions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917761711603712 |
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| author | Pain, Jean-Christophe |
| author_facet | Pain, Jean-Christophe |
| contents | We propose a sum rule for $r$-derangements (meaning that the elements are restricted to be in distinct cycles in the cycle decomposition) involving binomial coefficients. The identity, obtained using the Cauchy product of two exponential generating functions, generalizes a known relation for usual derangements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15927 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A sum rule for $r$-derangements obtained from the Cauchy product of exponential generating functions Pain, Jean-Christophe Combinatorics We propose a sum rule for $r$-derangements (meaning that the elements are restricted to be in distinct cycles in the cycle decomposition) involving binomial coefficients. The identity, obtained using the Cauchy product of two exponential generating functions, generalizes a known relation for usual derangements. |
| title | A sum rule for $r$-derangements obtained from the Cauchy product of exponential generating functions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.15927 |