Conference paper
A characterization of fine words over a finite alphabet
International school and conference on Combinatorics, Automata and Number Theory (Liege, Belgium, 08/05/2006–09/05/2006)
2006
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.
Details
- Title
- A characterization of fine words over a finite alphabet
- Authors/Creators
- A. Glen (Author/Creator)
- Conference
- International school and conference on Combinatorics, Automata and Number Theory (Liege, Belgium, 08/05/2006–09/05/2006)
- Identifiers
- 991005541759007891
- Murdoch Affiliation
- Murdoch University
- Language
- English
- Resource Type
- Conference paper
- Note
- See journal article at http://researchrepository.murdoch.edu.au/3878/
Metrics
194 File views/ downloads
61 Record Views