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
How many squares can a string contain?
Journal of Combinatorial Theory Series A
On Maximal Repetitions in Words
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
European Journal of Combinatorics
Finding Maximal Repetitions in a Word in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A simple proof that a word of length n has at most 2n distinct squares
Journal of Combinatorial Theory Series A
A note on the number of squares in a word
Theoretical Computer Science
The number of runs in a string
Information and Computation
Maximal repetitions in strings
Journal of Computer and System Sciences
How many runs can a string contain?
Theoretical Computer Science
Towards a Solution to the "Runs" Conjecture
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
The Number of Runs in Sturmian Words
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Language and Automata Theory and Applications
On the Maximal Number of Cubic Subwords in a String
Combinatorial Algorithms
The number of runs in a string: improved analysis of the linear upper bound
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
A d-step approach to the maximum number of distinct squares and runs in strings
Discrete Applied Mathematics
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We investigate the problem of the maximum number of different cubic subwords (of the form www) in a given word. We also consider square subwords (of the form ww). The problem of the maximum number of squares in a word is not well understood. Several new results related to this problem are presented in the paper. We consider two simple problems related to the maximum number of subwords which are squares or which are highly repetitive; then we provide a nontrivial estimation for the number of cubes. We show that the maximum number of squares xx such that x is not a primitive word (nonprimitive squares) in a word of length n is exactly @?n2@?-1, and the maximum number of subwords of the form x^k, for k=3, is exactly n-2. In particular, the maximum number of cubes in a word is not greater than n-2 either. Using properties of occurrences of cubes, we improve this bound significantly. We show that the maximum number of cubes in a word of length n is between 12n-2n and 45n.