Permutations avoiding an increasing number of length-increasing forbidden subsequences

Elena Barcucci 1 Alberto Del Lungo 1 Elisa Pergola 1 Renzo Pinzani 1
1 DSI - Dipartimento di Sistemi e Informatica
Abstract : A permutation π is said to be τ -avoiding if it does not contain any subsequence having all the same pairwise comparisons as τ . This paper concerns the characterization and enumeration of permutations which avoid a set F^j of subsequences increasing both in number and in length at the same time. Let F^j be the set of subsequences of the form σ (j+1)(j+2), σ being any permutation on \1,...,j\. For j=1 the only subsequence in F^1 is 123 and the 123-avoiding permutations are enumerated by the Catalan numbers; for j=2 the subsequences in F^2 are 1234 2134 and the (1234,2134)avoiding permutations are enumerated by the Schröder numbers; for each other value of j greater than 2 the subsequences in F^j are j! and their length is (j+2) the permutations avoiding these j! subsequences are enumerated by a number sequence \a_n\ such that C_n ≤ a_n ≤ n!, C_n being the nth Catalan number. For each j we determine the generating function of permutations avoiding the subsequences in F^j according to the length, to the number of left minima and of non-inversions.
Keywords : Permutations Forbidden subsequences Catalan numbers Schröder numbers
Type de document :
Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2000, 4 (1), pp.31-44
Liste complète des métadonnées

Littérature citée [29 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/hal-00958943
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Soumis le : jeudi 13 mars 2014 - 16:49:40
Dernière modification le : mercredi 29 novembre 2017 - 10:26:19
Document(s) archivé(s) le : vendredi 13 juin 2014 - 12:02:39

Fichier

dm040103.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00958943, version 1

Collections

TDS-MACS

Citation

Elena Barcucci, Alberto Del Lungo, Elisa Pergola, Renzo Pinzani. Permutations avoiding an increasing number of length-increasing forbidden subsequences. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2000, 4 (1), pp.31-44. 〈hal-00958943〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

119

Téléchargements de fichiers

138

Contact


archive-ouverte@inria.fr