Berthé, Valérie; Vuillon, Laurent Tilings and rotations on the torus: A two-dimensional generalization of Sturmian sequences. (English) Zbl 0970.68124 Discrete Math. 223, No. 1-3, 27-53 (2000). 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. Cited in 4 ReviewsCited in 46 Documents MSC: 68R15 Combinatorics on words Keywords:Sturmian sequences PDF BibTeX XML Cite \textit{V. Berthé} and \textit{L. Vuillon}, Discrete Math. 223, No. 1--3, 27--53 (2000; Zbl 0970.68124) Full Text: DOI OpenURL