Elsevier

Discrete Mathematics

Volume 308, Issue 11, 6 June 2008, Pages 2261-2264
Discrete Mathematics

Unbordered factors and Lyndon words

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Abstract

A primitive word w is a Lyndon word if w is minimal among all its conjugates with respect to some lexicographic order. A word w is bordered if there is a nonempty word u such that w=uvu for some word v. A right extension of a word w of length n is a word wu where all factors longer than n are bordered. A right extension wu of w is called trivial if there exists a positive integer k such that wk=uv for some word v.

We prove that Lyndon words have only trivial right extensions. Moreover, we give a conjecture which characterizes a property of every word w which has a nontrivial right extension of length 2|w|-2.

Keywords

Combinatorics on words
Duval's conjecture
Lyndon words
Unbordered factors
Sturmian words

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