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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have