On the distribution of characteristic parameters of words II

¹ Dipartimento di Matematica e Informatica, Università di Perugia, via Vanvitelli 1, 06123 Perugia, Italy; carpi@dipmat.unipg.it.
² Dipartimento di Matematica dell'Università di Roma “La Sapienza”, piazzale Aldo Moro 2, 00185 Roma, Italy and Centro Interdisciplinare “B. Segre”, Accademia dei Lincei, via della Lungara 10, 00100 Roma, Italy; deluca@mat.uniroma1.it.

Received: 15 November 2001
Accepted: 27 May 2002

Abstract

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.