On the distribution of characteristic parameters of words II

Carpi, Arturo; Luca, Aldo de

doi:10.1051/ita:2002005

Carpi, Arturo ; Luca, Aldo de

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 1, pp. 97-127.

Résumé

The characteristic parameters $K_{w}$ and $R_{w}$ of a word $w$ over a finite alphabet are defined as follows: $K_{w}$ is the minimal natural number such that $w$ has no repeated suffix of length $K_{w}$ and $R_{w}$ is the minimal natural number such that $w$ has no right special factor of length $R_{w}$ . 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 $n$ .

MR Zbl | 2 citations dans Numdam

DOI : 10.1051/ita:2002005

Classification : 68R15, 68R05
Mots clés : special factor, characteristic parameter, repeated factor

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     title = {On the distribution of characteristic parameters of words {II}},
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     publisher = {EDP-Sciences},
     volume = {36},
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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://www.numdam.org/articles/10.1051/ita:2002005/

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