On the Adjacent Cycle Derangements

الملخص EN

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.