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arXiv · 2402.16160

The Hankel determinants for the generalized derangement polynomials of order r

Ghania Guettai·Diffalah Laissaoui·Mourad Rahmani
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Abstract

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.

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Ghania Guettai, Diffalah Laissaoui, Mourad Rahmani. 2024-02-25. The Hankel determinants for the generalized derangement polynomials of order r. https://arxiv.org/abs/2402.16160

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