The Hankel determinants for the generalized derangement polynomials of order r
Combinatorics
2024-02-27 v1
Abstract
This paper sets out to introduce the generalized derangement polynomials of order . It then proceeds to establish various identities associated with these polynomials, along with providing recurrence relations for derangement polynomials of order . Additionally, the paper offers a probabilistic approach for the generalized derangement polynomials of order . Furthermore, it furnishes a clear expression for the Hankel determinants pertaining to these generalized derangement polynomials of order , and subsequently infers the Hankel determinants for derangement polynomials of the same order, as well as for the count of cyclic derangements.
Keywords
Cite
@article{arxiv.2402.16160,
title = {The Hankel determinants for the generalized derangement polynomials of order r},
author = {Ghania Guettai and Diffalah Laissaoui and Mourad Rahmani},
journal= {arXiv preprint arXiv:2402.16160},
year = {2024}
}