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Some Identities on Derangement and Degenerate Derangement Polynomials

  • Taekyun Kim
  • Dae San Kim
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the nth derangement number. In this paper, as natural companions to derangement numbers and degenerate versions of the companions we introduce derangement polynomials and degenerate derangement polynomials. We give some of their properties, recurrence relations, and identities for those polynomials which are related to some special numbers and polynomials.

Keywords

Derangement polynomials Degenerate derangement polynomials 

2010 Mathematices Subject Classification

11B83 11B73 05A19 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsCollege of Science Tianjin Polytechnic UniversityTianjinChina
  2. 2.Department of MathematicsKwangwoon UniversitySeoulRepublic of Korea
  3. 3.Department of MathematicsSogang UniversitySeoulRepublic of Korea

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