Counting and generating permutations using timed languages (long version)

Abstract : The signature of a permutation $\sigma$ is a word whose letter of index i is d when $sigma$ has a descent (i.e. $\sigma(i)>\sigma(i+1)$) and is a when $\sigma$ has an ascent (i.e. $\sigma(i)<\sigma(i+1)$). Combinatorics of permutations with a prescribed signature is quite well explored. Given a language over the alphabet {a,d}, we associate to it the class of permutations with signature in the language. Here we state and address the two problems of counting and randomly generating for every classes of permutations associated to a regular language. First we give an algorithm that computes a closed form formula for the exponential generating function of such a class. Then we give an algorithm that given a regular language L and an integer n generates randomly the n-length permutations of the class associated to L in a uniform manner, i.e. all the permutations of length n with signature in L are equally probable to be returned. Both contributions are based on a geometric interpretation of a subclass of regular timed languages.
Type de document :
Pré-publication, Document de travail
2013


https://hal-upec-upem.archives-ouvertes.fr/hal-00820373
Contributeur : Nicolas Basset <>
Soumis le : mercredi 2 octobre 2013 - 10:59:36
Dernière modification le : mardi 11 octobre 2016 - 13:55:57

Fichier

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

Identifiants

  • HAL Id : hal-00820373, version 2

Citation

Nicolas Basset. Counting and generating permutations using timed languages (long version). 2013. <hal-00820373v2>

Exporter

Partager

Métriques

Consultations de
la notice

249

Téléchargements du document

96