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2004
Springer

A Generalization of Repetition Threshold

9 years 16 days ago
A Generalization of Repetition Threshold
Brandenburg and (implicitly) Dejean introduced the concept of repetition threshold: the smallest real number α such that there exists an infinite word over a k-letter alphabet that avoids β-powers for all β > α. We generalize this concept to include the lengths of the avoided words. We give some conjectures supported by numerical evidence and prove some of these conjectures. As a consequence of one of our results, we show that the pattern ABCBABC is 2-avoidable. This resolves a question left open in Cassaigne’s thesis. Key words: Combinatorics on words, Repetitions
Lucian Ilie, Pascal Ochem, Jeffrey Shallit
Added 02 Jul 2010
Updated 02 Jul 2010
Type Conference
Year 2004
Where MFCS
Authors Lucian Ilie, Pascal Ochem, Jeffrey Shallit
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