On the Adjacent Cycle Derangements | Zendy

L. de Francesco Albasini | Zendy; Norma Zagaglia Salvi | Zendy

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On the Adjacent Cycle Derangements

Author(s) -

L. de Francesco Albasini,

Norma Zagaglia Salvi

Publication year - 2012

Publication title -

isrn discrete mathematics

Language(s) - English

Resource type - Journals

ISSN - 2090-7788

DOI - 10.5402/2012/340357

Subject(s) - derangement , multiset , permutation (music) , bijection , combinatorics , mathematics , set (abstract data type) , mathematical proof , interpretation (philosophy) , finite set , combinatorial proof , discrete mathematics , computer science , physics , mathematical analysis , geometry , acoustics , programming language

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.

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