An O(n log n) algorithm for finding all repetitions in a string
Journal of Algorithms
Detecting leftmost maximal periodicities
Discrete Applied Mathematics - Combinatorics and complexity
Text algorithms
Cantor sets and Dejean's conjecture
Journal of Automata, Languages and Combinatorics - Special issue: Second international conference developments in language theory
How many squares can a string contain?
Journal of Combinatorial Theory Series A
The exact number of squares in Fibonacci words
Theoretical Computer Science
A Periodicity Theorem on Words and Applications
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Computation of Squares in a String (Preliminary Version)
CPM '94 Proceedings of the 5th Annual Symposium on Combinatorial Pattern Matching
Simple and Flexible Detection of Contiguous Repeats Using a Suffix Tree (Preliminary Version)
CPM '98 Proceedings of the 9th Annual Symposium on Combinatorial Pattern Matching
Binary Patterns in Infinite Binary Words
Formal and Natural Computing - Essays Dedicated to Grzegorz Rozenberg [on occasion of his 60th birthday, March 14, 2002]
Finding Approximate Repetitions under Hamming Distance
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
The Number of Runs in Sturmian Words
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
On the maximum number of cubic subwords in a word
European Journal of Combinatorics
A computational framework for determining run-maximal strings
Journal of Discrete Algorithms
Computing the number of cubic runs in standard Sturmian words
Discrete Applied Mathematics
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A (fractional) repetition in a word w is a subword with the period of at most half of the subword length. We study maximal repetitions occurring in w, that is those for which any extended subword of w has a bigger period. The set of such repetitions represents in a compact way all repetitions in w. We first study maximal repetitions in Fibonacci words - we count their exact number, and estimate the sum of their exponents. These quantities turn out to be linearly-bounded in the length of the word. We then prove that the maximal number of maximal repetitions in general words (on arbitrary alphabet) of length n is linearly-bounded in n, and we mention some applications and consequences of this result.