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A characterization of fine words over a finite alphabet
Journal article   Open access   Peer reviewed

A characterization of fine words over a finite alphabet

A. Glen
Theoretical Computer Science, Vol.391(1-2), pp.51-60
2008
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Abstract

To any infinite word t over a finite alphabet A we can associate two infinite words min (t) and max (t) such that any prefix of min (t) (resp. max (t)) is the lexicographically smallest (resp. greatest) amongst the factors of t of the same length. We say that an infinite word t over A is fine if there exists an infinite word s such that, for any lexicographic order, min (t) = a s where a = min (A). In this paper, we characterize fine words; specifically, we prove that an infinite word t is fine if and only if t is either a strict episturmian word or a strict "skew episturmian word". This characterization generalizes a recent result of G. Pirillo, who proved that a fine word over a 2-letter alphabet is either an (aperiodic) Sturmian word, or an ultimately periodic (but not periodic) infinite word, all of whose factors are (finite) Sturmian.

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Citation topics
9 Mathematics
9.28 Pure Maths
9.28.534 Dynamical Systems
Web Of Science research areas
Computer Science, Theory & Methods
ESI research areas
Computer Science
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