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Combinatorial properties of infinite words associated with cut-and-project sequences

Louis-Sébastien GuimondZuzana MasákováEdita Pelantová — 2003

Journal de théorie des nombres de Bordeaux

The aim of this article is to study certain combinatorial properties of infinite binary and ternary words associated to cut-and-project sequences. We consider here the cut-and-project scheme in two dimensions with general orientation of the projecting subspaces. We prove that a cut-and-project sequence arising in such a setting has always either two or three types of distances between adjacent points. A cut-and-project sequence thus determines in a natural way a symbolic sequence (infinite word)...

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