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Words over an ordered alphabet and suffix permutations

Published online by Cambridge University Press:  15 December 2002

Jean-Pierre Duval  and
Arnaud Lefebvre
Jean-Pierre Duval
Affiliation:
LIFAR-ABISS, Faculté des Sciences, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France; jean-pierre.duval@univ-rouen.fr.
Arnaud Lefebvre
Affiliation:
ABISS, UMR 6037 du CNRS, Faculté des Sciences, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France; arnaud.lefebvre@univ-rouen.fr.
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Abstract

Given an ordered alphabet and a permutation, according to the lexicographic order, on the set of suffixes of a word w, we present in this article a linear time and space method to determine whether a word w' has the same permutation on its suffixes. Using this method, we are then also able to build the class of all the words having the same permutation on their suffixes, first of all the smallest one. Finally, we note that this work can lead to a method for generating a Lyndon word randomly in linear time or for computing the set of Lyndon words of length n .

Keywords

Suffix permutationLyndon words.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 3 , July 2002 , pp. 249 - 259
Copyright
© EDP Sciences, 2002

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References

M. Crochemore, C. Hancart and T. Lecroq, Algorithmique du texte. Vuibert (2001).
Duval, J.-P., Factorizing Words over an Ordered Alphabet. J. Algorithms 4 (1983) 363-381. CrossRef
McCreight, E.M., Space-Economical Suffix Tree Construction Al, Agorithm. J. Algorithms 23 (1976) 262-272.
C. Hohlweg and C. Reutenauer, Lyndon words, permutations and trees, Rapport interne 2002-017. Université Louis Pasteur de Strasbourg.