The Revisited q−Derangement Polynomials and Incomplete q−Derangement Polynomials

Year 2025, Volume: 17 Issue: 1, 17 - 25, 30.06.2025

Semra Kuş

https://doi.org/10.47000/tjmcs.1620260

https://izlik.org/JA25YJ88NU

Abstract

In this paper, the $q-$derangement polynomials of the second type $\mathfrak{d}_{\psi,q}(\gamma)$ and their generating function are defined. Subsequently, the incomplete $q-$derangement polynomials $d_{\psi,q}\left( \gamma,m\right)$ and numbers $d_{\psi,q}\left( m\right)$ are introduced, and various properties are derived. Furthermore, the relationship between the incomplete $q-$derangement numbers and $q-$ derangement numbers is demonstrated.

Keywords

Degenerate polynomials , q-analogue , recurrence relation

Ethical Statement

The author affirm that they adhered to scientific ethical principles during the research process and declare that there is no conflict of interest.

Supporting Institution

This study was not financially or otherwise supported by any institution or organization.

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