zbMATH — the first resource for mathematics

Tilings and rotations on the torus: A two-dimensional generalization of Sturmian sequences. (English) Zbl 0970.68124
Summary: We study a two-dimensional generalization of Sturmian sequences corresponding to an approximation of a plane: these sequences are defined on a three-letter alphabet and code a two-dimensional tiling obtained by projecting a discrete plane. We show that these sequences code a \(\mathbb{Z}^2\)-action generated by two rotations on the unit circle. We first deduce a new way of computing the rectangle complexity function. Then we provide an upper bound on the number of frequencies of rectangular factors of given size.

68R15 Combinatorics on words
Full Text: DOI