## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, September 02, 2003, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Dirk Nowotka (Turku University, Finland)

## Periodicity and Unbordered Words

A relationship between the length of a word and the maximum length of its unbordered factors will be presented in this talk.

Consider a finite word w of length n. We call a word bordered, if it has a proper prefix which is also a suffix of that word. Let f(w) denote the maximum length of all unbordered factors of w, and let p(w) denote the (shortest) period of w. Clearly, f(w) is less than or equal to p(w).

We establish that f(w) = p(w), if w has an unbordered prefix of length f(w) and n > 2 f(w) - 2. This bound is tight and solves the stronger version of a 21 years old conjecture by Duval. It follows from this result that, in general, n > 3 f(w) - 3 implies f(w) = p(w) which gives an improved bound for a question asked by Ehrenfeucht and Silberger in 1979.

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