On the adjacent cycle derangements. (English) Zbl 1258.05002

Summary: 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.


05A05 Permutations, words, matrices
05A15 Exact enumeration problems, generating functions
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