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On the combinatorics of derangements and related permutations

Author

Listed:
  • Zhang, Jie
  • Gray, Daniel
  • Wang, Hua
  • Zhang, Xiao-Dong

Abstract

A derangement is a permutation in which no entry is at its original position. The number of derangements of [n] is called the “derangement number” or “de Montmort number”, and is denoted by Dn. The sequence {Dn} enumerates, in addition to the number of derangements, many other permutations under various constraints. In this paper, we explore the connections between these combinatorial objects and provide bijective proofs. Some related enumerative problems are also mentioned.

Suggested Citation

  • Zhang, Jie & Gray, Daniel & Wang, Hua & Zhang, Xiao-Dong, 2022. "On the combinatorics of derangements and related permutations," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322004155
    DOI: 10.1016/j.amc.2022.127341
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