On maximal repetitions of arbitrary exponent

The first two authors have shown [1,2] (Kolpakov and Kucherov, 1999, 2000) that the sum of the exponents (and thus the number) of maximal repetitions of exponent at least 2 in a word (also called runs) is linear with respect to the length of the word. The exponent 2 in the definition of a run may seem arbitrary. In this paper, we consider maximal repetitions of exponent strictly greater than 1.