The characteristic parameters and of a word over a finite alphabet are defined as follows: is the minimal natural number such that has no repeated suffix of length and is the minimal natural number such that has no right special factor of length . In a previous paper, published on this journal, we have studied the distributions of these parameters, as well as the distribution of the maximal length of a repetition, among the words of each length on a given alphabet. In this paper we give the exact values of these distributions in a special case. However, these values give upper bounds to the distributions in the general case. Moreover, we study the most frequent and the average values of the characteristic parameters and of the maximal length of a repetition over the set of all words of length .
Mots-clés : special factor, characteristic parameter, repeated factor
@article{ITA_2002__36_1_97_0,
author = {Carpi, Arturo and Luca, Aldo de},
title = {On the distribution of characteristic parameters of words {II}},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {97--127},
publisher = {EDP-Sciences},
volume = {36},
number = {1},
year = {2002},
doi = {10.1051/ita:2002005},
mrnumber = {1928160},
zbl = {1052.68106},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ita:2002005/}
}
TY - JOUR AU - Carpi, Arturo AU - Luca, Aldo de TI - On the distribution of characteristic parameters of words II JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2002 SP - 97 EP - 127 VL - 36 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2002005/ DO - 10.1051/ita:2002005 LA - en ID - ITA_2002__36_1_97_0 ER -
%0 Journal Article %A Carpi, Arturo %A Luca, Aldo de %T On the distribution of characteristic parameters of words II %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2002 %P 97-127 %V 36 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2002005/ %R 10.1051/ita:2002005 %G en %F ITA_2002__36_1_97_0
Carpi, Arturo; Luca, Aldo de. On the distribution of characteristic parameters of words II. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 1, pp. 97-127. doi : 10.1051/ita:2002005. http://archive.numdam.org/articles/10.1051/ita:2002005/
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