Factors of generalised polynomials and automatic sequences

نویسندگان

  • Jakub Byszewski
  • Jakub Konieczny
چکیده

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.

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عنوان ژورنال:
  • CoRR

دوره abs/1802.02533  شماره 

صفحات  -

تاریخ انتشار 2018