Double Derangement Permutations  

作　　者：Pooya Daneshmand Kamyar Mirzavaziri Madjid Mirzavaziri Pooya Daneshmand;Kamyar Mirzavaziri;Madjid Mirzavaziri(Ferdowsi University of Mashhad, International Campus, Mashhad, Iran;National Organization for Development of Exceptional Talents (NODET) I, Mashhad, Iran;Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran)

机构地区：[1]Ferdowsi University of Mashhad, International Campus, Mashhad, Iran [2]National Organization for Development of Exceptional Talents (NODET) I, Mashhad, Iran [3]Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

出　　处：《Open Journal of Discrete Mathematics》2016年第2期99-104,共6页离散数学期刊（英文）

摘　　要：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  and  for , then  where .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  and  for , then  where .

关 键 词：Symmetric Group of Permutations Derangement Double Derangement 

分 类 号：O17[理学—数学]