On the sum of exponents of maximal repetitions in a word

This paper continues the study presented in {KolpakovKucherovRI98}, where it was proved that the number of maximal repetitions in a word is linearly-bounded in the word length. Here we strengthen this result and prove that the sum of exponents of maximal repetitions is linearly-bounded too. Similarly to {KolpakovKucherovRI98}, we first estimate the sum of exponents of maximal repetitions in Fibonacci words. Then we prove that the sum of exponents of all maximal repetitions in general words is linearly-bounded. Finally, some algorithmic applications of this results are discussed.