On the Adjacent Cycle Derangements

Luisa de Francesco Albasini, Norma Zagaglia Salvi
2012 ISRN Discrete Mathematics  
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.
doi:10.5402/2012/340357 fatcat:tuu5jumjx5a6bk2hw2yxbrdtmq