# A characterization of fine words over a finite alphabet

Glen, A.
(2006)
*A characterization of fine words over a finite alphabet.*
In: International school and conference on Combinatorics, Automata and Number Theory, 8 - 9 May, Liege, Belgium

## 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.

Publication Type: | Conference Paper |
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Conference Website: | http://www.cant.ulg.ac.be/cant2006/ |

Notes: | See journal article at http://researchrepository.murdoch.edu.au/3878/ |

URI: | http://researchrepository.murdoch.edu.au/id/eprint/3891 |

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