Properties of a Class of Toeplitz Words
Formal Languages and Automata Theory
2021-12-23 v1 Discrete Mathematics
Combinatorics
Abstract
We study the properties of the uncountable set of Stewart words. These are Toeplitz words specified by infinite sequences of Toeplitz patterns of the form , where is any permutation of the symbols 0,1,?. We determine the critical exponent of the Stewart words, prove that they avoid the pattern , find all factors that are palindromes, and determine their subword complexity. An interesting aspect of our work is that we use automata-theoretic methods and a decision procedure for automata to carry out the proofs.
Keywords
Cite
@article{arxiv.2112.12125,
title = {Properties of a Class of Toeplitz Words},
author = {Gabriele Fici and Jeffrey Shallit},
journal= {arXiv preprint arXiv:2112.12125},
year = {2021}
}