Table of Contents
ISRN Discrete Mathematics
Volume 2012 (2012), Article ID 340357, 12 pages
http://dx.doi.org/10.5402/2012/340357
Research Article

On the Adjacent Cycle Derangements

Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

Received 28 September 2012; Accepted 29 October 2012

Academic Editors: S. Locke, Y. Manoussakis, and X. Yong

Copyright © 2012 Luisa de Francesco Albasini and Norma Zagaglia Salvi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A derangement, that is, a permutation without fixed points, of a finite set is said to be an adjacent cycle when all its cycles are formed by a consecutive set of integers. In this paper we determine enumerative properties of these permutations using analytical and bijective proofs. Moreover a combinatorial interpretation in terms of linear species is provided. Finally we define and investigate the case of the adjacent cycle derangements of a multiset.