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 .