On the distribution of characteristic parameters of words II

The characteristic parameters Kw and Rw of a word w over a finite alphabet are defined as follows: Kw is the minimal natural number such that w has no repeated suffix of length Kw and Rw is the minimal natural number such that w has no right special factor of length Rw. 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. Mathematics Subject Classification. 68R15, 68R05. Introduction In a recent paper [4], which hereafter will be also referred to as CP, we have studied some properties of the distributions of two basic parameters which can be associated with any finite word w on a given alphabet A. These parameters, called characteristic parameters and denoted by Kw and Rw, are defined as follows: Kw is the length of the shortest unrepeated suffix of w and Rw is the minimal natural