×
de Francesco Albasini, Luisa; Salvi, Norma Zagaglia

On the adjacent cycle derangements. (English) Zbl 1258.05002

ISRN Discrete Math. 2012, Article ID 340357, 12 p. (2012).
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.

MSC:

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

Keywords:

derangement; permutation without fixed points; cycles; enumerative properties; analytical proofs; bijective proofs; linear species; adjacent cycle derangements; multiset
PDF BibTeX XML Cite
\textit{L. de Francesco Albasini} and \textit{N. Z. Salvi}, ISRN Discrete Math. 2012, Article ID 340357, 12 p. (2012; Zbl 1258.05002)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] R. A. Brualdi and E. Deutsch, “Adjacent q-cycles in permutations,” Annals of Combinatorics, vol. 16, no. 2, pp. 203-213, 2012. · Zbl 1256.05003
[2] N. Zagaglia Salvi, “Adjacent-cycle permutations of a multiset,” Advances and Applications in Discrete Mathematics, vol. 8, no. 2, pp. 65-74, 2011. · Zbl 1238.05006
[3] A. Joyal, “Une théorie combinatoire des séries formelles,” Advances in Mathematics, vol. 42, no. 1, pp. 1-82, 1981. · Zbl 0491.05007
[4] O. M. D’Antona and E. Munarini, “A combinatorial interpretation of punctured partitions,” Journal of Combinatorial Theory, Series A, vol. 91, no. 1-2, pp. 264-282, 2000. · Zbl 0963.05012
[5] D. E. Knuth, The Art of Computer Programming: Volume 3, Sorting and searching, Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley, Reading, Mass, USA, 1973. · Zbl 0302.68010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.