Entropy and diffraction of the $k$-free points in $n$-dimensional lattices

Abstract

We consider the $k$th-power-free points in $n$-dimensional lattices and explicitly calculate their entropies and diffraction spectra. This is of particular interest since these sets have holes of unbounded inradius.

27 pages, 2 figures; revised version with new references [7,8,23]; latest version with new Theorem 6 and updated reference [7]

References in corpus (1)

• Kinematic Diffraction from a Mathematical Viewpoint

Cited by in corpus (12)

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• Scaling of diffraction intensities near the origin: Some rigorous results
• Radial spacing distributions from planar points sets
• Dynamical properties of $k$-free lattice points
• Model sets with positive entropy in Euclidean cut and project schemes
• Model sets with precompact Borel windows
• Dynamical spectrum of power-free integers in quadratic number fields and beyond
• Scaling of the diffraction measure of $k$-free integers near the origin