Zola's Repetitions: On Repetition in Zola

On Maximal Repetitions in Words

Axel Thue's Work on Repetitions in Words

The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched.

On primary and secondary repetitions in words

Combinatorial properties of maximal repetitions (runs) in formal words are studied. We classify all maximal repetitions in a word as primary and secondary where the set of all primary repetitions determines all the other repetitons in the word. Essential combinatorial properties of primary repetitions are established.

Two-Pattern Strings — Computing Repetitions & Near-Repetitions

In a recent paper we introduced infinite two-pattern strings on the alphabet {a, b} as a generalization of Sturmian strings, and we posed three questions about them: • Given a finite string x, can we in linear time O(|x|) recognize whether or not x is a prefix/substring of some infinite two-pattern string? • If recognized as two-pattern, can all the repetitions in x be computed in linear time? ...

Maximal repetitions in strings

The cornerstone of any algorithm computing all repetitions in strings of length n in O(n) time is the fact that the number of maximal repetitions (runs) is linear. Therefore, the most important part of the analysis of the running time of such algorithms is counting the number of runs. Kolpakov and Kucherov [FOCS’99] proved it to be cn but could not provide any value for c. Recently, Rytter [STA...