Decision Algorithms for Fibonacci-Automatic Words, with Applications to Pattern Avoidance
Abstract
We implement a decision procedure for answering questions about a class of infinite words that might be called (for lack of a better name) "Fibonacci-automatic". This class includes, for example, the famous Fibonacci word f = 01001010..., the fixed point of the morphism 0 -> 01 and 1 -> 0. We then recover many results about the Fibonacci word from the literature (and improve some of them), such as assertions about the occurrences in f of squares, cubes, palindromes, and so forth. As an application of our method we prove a new result: there exists an aperiodic infinite binary word avoiding the pattern x x x^R. This is the first avoidability result concerning a nonuniform morphism proven purely mechanically.
Cite
@article{arxiv.1406.0670,
title = {Decision Algorithms for Fibonacci-Automatic Words, with Applications to Pattern Avoidance},
author = {Chen Fei Du and Hamoon Mousavi and Luke Schaeffer and Jeffrey Shallit},
journal= {arXiv preprint arXiv:1406.0670},
year = {2014}
}
Comments
inserted new section 9 on abelian properties