Repetition threshold for circular words
type: Item
instance of: scholarly article
title: Repetition threshold for circular words
zbMATH Open document ID: 1266.68148
author: Irina A. Gorbunova
published in: The Electronic Journal of Combinatorics
publication date: 2013-06-07T00:00:00Z
full work available at URL: v19i4p11
review text: Summary: We find the threshold between avoidable and unavoidable repetitions in circular words over \(k\) letters for any \(k\geq6\). Namely, we show that the number CRT\((k)=\frac{\left\lceil {k/2}\right\rceil{+}1}{\left\lceil {k/2}\right\rceil}\) satisfies the following properties. For any \(n\) there exists a \(k\)-ary circular word of length \(n\) containing no repetition of exponent greater than CRT\((k)\). On the other hand, \(k\)-ary circular words of some lengths must have a repetition of exponent at least CRT\((k)\).
Mathematics Subject Classification ID: 68R15
zbMATH DE Number: 6171794
zbMATH Keywords: Dejean's conjecture
zbMATH Keywords: repetition threshold
zbMATH Keywords: circular words
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6171794