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
Linear time algorithms for finding and representing all the tandem repeats in a string
Journal of Computer and System Sciences
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
Maximal repetitions in strings
Journal of Computer and System Sciences
A fast algorithm for finding the positions of all squares in a run-length encoded string
Theoretical Computer Science
Hi-index | 5.23 |
Squares are strings of the form ww where w is any nonempty string. Two squares ww and w^'w^' are of different types if and only if ww^'. Fraenkel and Simpson [Avieri S. Fraenkel, Jamie Simpson, How many squares can a string contain? Journal of Combinatorial Theory, Series A 82 (1998) 112-120] proved that the number of square types contained in a string of length n is bounded by O(n). The set of all different square types contained in a string is called the vocabulary of the string. If a square can be obtained by a series of successive right-rotations from another square, then we say the latter covers the former. A square is called a c-square if no square with a smaller index can cover it and it is not a trivial square. The set containing all c-squares is called the covering set. Note that every string has a unique covering set. Furthermore, the vocabulary of the covering set are called c-vocabulary. In this paper, we prove that the cardinality of c-vocabulary in a string is less than 143N, where N is the number of runs in this string.