Double Derangement Permutations - Open Journal of Discrete Mathematics

OJDM > Vol.6 No.2, April 2016

Open Journal of Discrete Mathematics

Volume 6, Issue 2 (April 2016)

ISSN Print: 2161-7635 ISSN Online: 2161-7643

Google-based Impact Factor: 0.64 Citations

Double Derangement Permutations ()

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DOI: 10.4236/ojdm.2016.62010 2,375 Downloads 4,356 Views

Author(s)

Pooya Daneshmand¹, Kamyar Mirzavaziri², Madjid Mirzavaziri^3*

Affiliation(s)

¹Ferdowsi University of Mashhad, International Campus, Mashhad, Iran.
²National Organization for Development of Exceptional Talents (NODET) I, Mashhad, Iran.
³Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.

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

and

for

, then

where

KEYWORDS

Symmetric Group of Permutations, Derangement, Double Derangement

Share and Cite:

Daneshmand, P. , Mirzavaziri, K. and Mirzavaziri, M. (2016) Double Derangement Permutations. Open Journal of Discrete Mathematics, 6, 99-104. doi: 10.4236/ojdm.2016.62010.

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