On degenerate multi-poly-derangement polynomials and numbers

Abstract

The problem of counting derangements was begun in 1708 by Pierre R[Formula: see text]mond de Montmort (see [Carlitz. The number of derangements of a sequence with given specification. Fibonacci Quart. 1978;16:255–258], [Clarke and Sved. Derangements and Bell numbers. Math Mag. 1993;66:299–303]), and its applications have been investigated actively by many researchers. In this paper, we study properties of the degenerate multi-poly-derangement polynomials and numbers that are defined by using the multiple logarithm function, and derive some interesting identities related to these polynomials and numbers.

Keywords

• Derangement polynomials
• multiple logarithm
• the Stirling number of the first kind and the second kind
• λ-analogue of the Stirling numbers of the first and the second kind
• degenerate exponential functions
• 11B73