Factors of generalised polynomials and automatic sequences.
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.
Publisher URL: http://arxiv.org/abs/1802.02533
DOI: arXiv:1802.02533v1
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