Some results on the number of periodic factors in words

Abstract The exponent of a word is the relation between its length and its minimal period. A repetition (subrepetition) in a word is a factor of exponent not less than 2 (less than 2). A gapped repeat in a word is a pair of identical factors with a positive gap between these factors. In the paper a review of some recent results concerning the number of repetitions, subrepetitions and gapped repeats in words of fixed length is presented.

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