Open and Closed Prefixes of Sturmian Words
Combinatorics
2014-07-15 v1 Discrete Mathematics
Formal Languages and Automata Theory
Abstract
A word is closed if it contains a proper factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We deal with the sequence of open and closed prefixes of Sturmian words and prove that this sequence characterizes every finite or infinite Sturmian word up to isomorphisms of the alphabet. We then characterize the combinatorial structure of the sequence of open and closed prefixes of standard Sturmian words. We prove that every standard Sturmian word, after swapping its first letter, can be written as an infinite product of squares of reversed standard words.
Keywords
Cite
@article{arxiv.1306.2254,
title = {Open and Closed Prefixes of Sturmian Words},
author = {Alessandro De Luca and Gabriele Fici},
journal= {arXiv preprint arXiv:1306.2254},
year = {2014}
}
Comments
To appear in WORDS 2013 proceedings