# 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

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topDuval, 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

top- [1] M. Crochemore, C. Hancart and T. Lecroq, Algorithmique du texte. Vuibert (2001). Zbl1134.68300
- [2] J.-P. Duval, Factorizing Words over an Ordered Alphabet. J. Algorithms 4 (1983) 363-381. Zbl0532.68061MR729232
- [3] E.M. McCreight, A Space-Economical Suffix Tree Construction Algorithm. J. Algorithms 23 (1976) 262-272. Zbl0329.68042MR413594
- [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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