Factors of generalised polynomials and automatic sequences
Combinatorics
2018-02-08 v1 Formal Languages and Automata Theory
Dynamical Systems
Abstract
The aim of this short note is to generalise the result of Rampersad--Shallit saying that an automatic sequence and a Sturmian sequence cannot have arbitrarily long common factors. We show that the same result holds if a Sturmian sequence is replaced by an arbitrary sequence whose terms are given by a generalised polynomial (i.e., an expression involving algebraic operations and the floor function) that is not periodic except for a set of density zero.
Cite
@article{arxiv.1802.02533,
title = {Factors of generalised polynomials and automatic sequences},
author = {Jakub Byszewski and Jakub Konieczny},
journal= {arXiv preprint arXiv:1802.02533},
year = {2018}
}
Comments
6 pages