5-Abelian cubes are avoidable on binary alphabets∗∗∗. (31st July 2014)

• Record Type: Journal Article
• Authors: Mercaş, Robert; Saarela, Aleksi
• Is Part Of: RAIRO. Volume 48:Number 4(2014)
• Page Start: 467
• Page End: 478
• Publication Date: 2014-07-31
• Subjects: Machine theory -- Periodicals; Electronic data processing -- Periodicals; 004.05
• DOI: 10.1051/ita/2014020
• Languages: English
• ISSNs: 0988-3754

Abstract

<abstract abstract-type="normal" xml:lang="en"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>A <italic>k</italic>-abelian cube is a word <italic>uvw</italic>, where the factors <italic>u</italic>, <italic>v</italic>, and <italic>w</italic> are either pairwise equal, or have the same multiplicities for every one of their factors of length at most <italic>k</italic>. Previously it has been shown that <italic>k</italic>-abelian cubes are avoidable over a binary alphabet for <italic>k</italic> ≥ 8. Here it is proved that this holds for <italic>k</italic> ≥ 5.</p> </abstract>