English

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 rr . It then proceeds to establish various identities associated with these polynomials, along with providing recurrence relations for derangement polynomials of order r r. Additionally, the paper offers a probabilistic approach for the generalized derangement polynomials of order rr . Furthermore, it furnishes a clear expression for the Hankel determinants pertaining to these generalized derangement polynomials of order rr, 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}
}