On the Adjacent Cycle Derangements. (2nd December 2012)

• Record Type: Journal Article
• Authors: de Francesco Albasini, Luisa; Zagaglia Salvi, Norma
• Other Names: Locke S. Academic Editor.; Manoussakis Y. Academic Editor.; Yong X. Academic Editor.
• Is Part Of: ISRN discrete mathematics. Volume 2012(2012)
• Publication Date: 2012-12-02
• Subjects: Discrete mathematics -- Periodicals; Computer science -- Mathematics; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.5402/2012/340357
• Languages: English
• ISSNs: 2090-7788

Abstract

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.