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Distribution of points of one-dimensional quasilattices with respect to a variable module. (English. Russian original) Zbl 1347.11017
Russ. Math. 56, No. 3, 14-19 (2012); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2012, No. 3, 17-23 (2012).
Summary: We consider one-dimensional quasiperiodic Fibonacci tilings. Namely, we study sets of vertices of these tilings that represent one-dimensional quasilattices defined on the base of a parameterization by rotations of a circle, and the distribution of points of quasilattices with respect to a variable module. We show that the distribution with respect to some modules is not uniform. We describe the distribution function and its integral representation, and estimate the remainder in the problem of the distribution of points of a quasilattice for corresponding modules.

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B83 Special sequences and polynomials
05B45 Combinatorial aspects of tessellation and tiling problems
Full Text: DOI
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