Words over an ordered alphabet and suffix permutations

Jean-Pierre Duval; Arnaud Lefebvre

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2002)

  • Volume: 36, Issue: 3, page 249-259
  • ISSN: 0988-3754

Abstract

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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 .

How to cite

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Duval, Jean-Pierre, and Lefebvre, Arnaud. "Words over an ordered alphabet and suffix permutations." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 36.3 (2002): 249-259. <http://eudml.org/doc/245928>.

@article{Duval2002,
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 $w^\{\prime \}$ 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 $n$.},
author = {Duval, Jean-Pierre, Lefebvre, Arnaud},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {suffix permutation; Lyndon words; permutation; Lyndon word},
language = {eng},
number = {3},
pages = {249-259},
publisher = {EDP-Sciences},
title = {Words over an ordered alphabet and suffix permutations},
url = {http://eudml.org/doc/245928},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Duval, Jean-Pierre
AU - Lefebvre, Arnaud
TI - Words over an ordered alphabet and suffix permutations
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 3
SP - 249
EP - 259
AB - 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 $w^{\prime }$ 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 $n$.
LA - eng
KW - suffix permutation; Lyndon words; permutation; Lyndon word
UR - http://eudml.org/doc/245928
ER -

References

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  1. [1] M. Crochemore, C. Hancart and T. Lecroq, Algorithmique du texte. Vuibert (2001). Zbl1134.68300
  2. [2] J.-P. Duval, Factorizing Words over an Ordered Alphabet. J. Algorithms 4 (1983) 363-381. Zbl0532.68061MR729232
  3. [3] E.M. McCreight, A Space-Economical Suffix Tree Construction Algorithm. J. Algorithms 23 (1976) 262-272. Zbl0329.68042MR413594
  4. [4] C. Hohlweg and C. Reutenauer, Lyndon words, permutations and trees, Rapport interne 2002-017. Université Louis Pasteur de Strasbourg. Zbl1058.68086MR2022847

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