A note on some identities of derangement polynomials
The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708 (see Carlitz in Fibonacci Q. 16(3):255–258, 1978, Clarke and Sved in Math. Mag. 66(5):299–303, 1993, Kim, Kim and Kwon in Adv. Stud. Contemp. Math. (Kyungshang) 28(1):1–11 2018. A derangement is a permutation tha... Full description
Journal Title:  Journal of Inequalities and Applications 2018, Vol.2018(1), pp.117 
Main Author:  Kim, Taekyun 
Other Authors:  Kim, Dae , Jang, GwanWoo , Kwon, Jongkyum 
Format:  Electronic Article 
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English 
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ID:  EISSN: 1029242X ; DOI: 10.1186/s1366001816368 
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recordid:  springer_jour10.1186/s1366001816368 
title:  A note on some identities of derangement polynomials 
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ispartof:  Journal of Inequalities and Applications, 2018, Vol.2018(1), pp.117 
description:  The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708 (see Carlitz in Fibonacci Q. 16(3):255–258, 1978, Clarke and Sved in Math. Mag. 66(5):299–303, 1993, Kim, Kim and Kwon in Adv. Stud. Contemp. Math. (Kyungshang) 28(1):1–11 2018. A derangement is a permutation that has no fixed points, and the derangement number d n $d_{n}$ is the number of fixedpointfree permutations on an n element set. In this paper, we study the derangement polynomials and investigate some interesting properties which are related to derangement numbers. Also, we study two generalizations of derangement polynomials, namely higherorder and r derangement polynomials, and show some relations between them. In addition, we express several special polynomials in terms of the higherorder derangement polynomials by using umbral calculus. 
language:  eng 
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identifier:  EISSN: 1029242X ; DOI: 10.1186/s1366001816368 
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