Reversible Christoffel factorizations
Discrete Mathematics
2013-07-12 v2 Formal Languages and Automata Theory
Combinatorics
Abstract
We define a family of natural decompositions of Sturmian words in Christoffel words, called *reversible Christoffel* (RC) factorizations. They arise from the observation that two Sturmian words with the same language have (almost always) arbitrarily long Abelian equivalent prefixes. Using the three gap theorem, we prove that in each RC factorization, only 2 or 3 distinct Christoffel words may occur. We begin the study of such factorizations, considered as infinite words over 2 or 3 letters, and show that in the general case they are either Sturmian words, or obtained by a three-interval exchange transformation.
Cite
@article{arxiv.1211.3049,
title = {Reversible Christoffel factorizations},
author = {Michelangelo Bucci and Alessandro De Luca and Luca Q. Zamboni},
journal= {arXiv preprint arXiv:1211.3049},
year = {2013}
}
Comments
12 pages, submitted. Previous draft presented at RuFiDiM 2011