WORD COMPLEXITY AND REPETITIONS IN WORDS

Word Complexity And Repetitions In Words

With ideas from data compression and combinatorics on words, we introduce a complexity measure for words, called repetition complexity, which quantifies the amount of repetition in a word. The repetition complexity of w, r(w), is defined as the smallest amount of space needed to store w when reduced by repeatedly applying the following procedure: n consecutive occurrences uu . . . u of the same...

On Maximal Repetitions in Words

Discovering Hidden Repetitions in Words

Pseudo-repetitions are a natural generalization of the classical notion of repetitions in sequences: they are the repeated concatenation of a word and its encoding under a certain morphism or antimorphism. We approach the problem of deciding whether there exists an anti-/morphism for which a word is a pseudo-repetition. In other words, we try to discover whether a word has a hidden repetitive s...

Abelian Repetitions in Partial Words∗

We study abelian repetitions in partial words, or sequences that may contain some unknown positions or holes. First, we look at the avoidance of abelian pth powers in infinite partial words, where p > 2, extending recent results regarding the case where p = 2. We investigate, for a given p, the smallest alphabet size needed to construct an infinite partial word with finitely or infinitely many ...

Abelian Repetitions in Sturmian Words

We investigate abelian repetitions in Sturmian words. We exploit a bijection between factors of Sturmian words and subintervals of the unitary segment that allows us to study the periods of abelian repetitions by using classical results of elementary Number Theory. If km denotes the maximal exponent of an abelian repetition of period m, we prove that lim sup km/m ≥ √ 5 for any Sturmian word, an...