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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.16160 |
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| _version_ | 1866911783970668544 |
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| author | Guettai, Ghania Laissaoui, Diffalah Rahmani, Mourad |
| author_facet | Guettai, Ghania Laissaoui, Diffalah Rahmani, Mourad |
| contents | This paper sets out to introduce the generalized derangement polynomials of order $r $. It then proceeds to establish various identities associated with these polynomials, along with providing recurrence relations for derangement polynomials of order $ r$. Additionally, the paper offers a probabilistic approach for the generalized derangement polynomials of order $r $. Furthermore, it furnishes a clear expression for the Hankel determinants pertaining to these generalized derangement polynomials of order $r$, and subsequently infers the Hankel determinants for derangement polynomials of the same order, as well as for the count of cyclic derangements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16160 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Hankel determinants for the generalized derangement polynomials of order r Guettai, Ghania Laissaoui, Diffalah Rahmani, Mourad Combinatorics 11B83, 05A15, 60C05, 05A19 This paper sets out to introduce the generalized derangement polynomials of order $r $. It then proceeds to establish various identities associated with these polynomials, along with providing recurrence relations for derangement polynomials of order $ r$. Additionally, the paper offers a probabilistic approach for the generalized derangement polynomials of order $r $. Furthermore, it furnishes a clear expression for the Hankel determinants pertaining to these generalized derangement polynomials of order $r$, and subsequently infers the Hankel determinants for derangement polynomials of the same order, as well as for the count of cyclic derangements. |
| title | The Hankel determinants for the generalized derangement polynomials of order r |
| topic | Combinatorics 11B83, 05A15, 60C05, 05A19 |
| url | https://arxiv.org/abs/2402.16160 |