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Graham, R.L., Knuth, D.E. and Patashnik, O. (1988) Concrete Mathematics. Addison-Wesley, Reading.

has been cited by the following article:

• TITLE: Double Derangement Permutations

  AUTHORS: Pooya Daneshmand, Kamyar Mirzavaziri, Madjid Mirzavaziri

  KEYWORDS: Symmetric Group of Permutations, Derangement, Double Derangement

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.6 No.2, April 12, 2016

  ABSTRACT: Let n be a positive integer. A permutation a of the symmetric group of permutations of is called a derangement if for each . Suppose that x and y are two arbitrary permutations of . We say that a permutation a is a double derangement with respect to x and y if and for each . In this paper, we give an explicit formula for , the number of double derangements with respect to x and y. Let and let and be two subsets of with and . Suppose that denotes the number of derangements x such that . As the main result, we show that if and z is a permutation such that for andfor , then where .