# Words over an ordered alphabet and suffix permutations

Jean-Pierre Duval; Arnaud Lefebvre

RAIRO - Theoretical Informatics and Applications (2010)

- 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 36.3 (2010): 249-259. <http://eudml.org/doc/92700>.

@article{Duval2010,

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
.
},

author = {Duval, Jean-Pierre, Lefebvre, Arnaud},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Suffix permutation; Lyndon words.; permutation; Lyndon word},

language = {eng},

month = {3},

number = {3},

pages = {249-259},

publisher = {EDP Sciences},

title = {Words over an ordered alphabet and suffix permutations},

url = {http://eudml.org/doc/92700},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Duval, Jean-Pierre

AU - Lefebvre, Arnaud

TI - Words over an ordered alphabet and suffix permutations

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

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' 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/92700

ER -

## References

top- M. Crochemore, C. Hancart and T. Lecroq, Algorithmique du texte. Vuibert (2001).
- J.-P. Duval, Factorizing Words over an Ordered Alphabet. J. Algorithms4 (1983) 363-381. Zbl0532.68061
- E.M. McCreight, A Space-Economical Suffix Tree Construction Algorithm. J. Algorithms23 (1976) 262-272. Zbl0329.68042
- C. Hohlweg and C. Reutenauer, Lyndon words, permutations and trees, Rapport interne 2002-017. Université Louis Pasteur de Strasbourg. Zbl1058.68086

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