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Dynamical Properties of k-Free Lattice Points

100%
Huck C., Baake M.
Acta Physica Polonica A
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2014
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vol. 126
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issue 2
482-485
EN
We revisit the visible points of a lattice in Euclidean n-space together with their generalisations, the k-th-power-free points of a lattice, and study the corresponding dynamical system that arises via the closure of the lattice translation orbit. Our analysis extends previous results obtained by Sarnak and by Cellarosi and Sinai for the special case of square-free integers and sheds new light on previous joint work with Peter Pleasants.
2
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Discrete Tomography: Magic Numbers for N-Fold Symmetry

81%
Huck C., Moll M., Nilsson J.
Acta Physica Polonica A
|
2014
|
vol. 126
|
issue 2
486-489
EN
We consider the problem of distinguishing convex subsets of n-cyclotomic model sets Λ by (discrete parallel) X-rays in prescribed Λ-directions. In this context, a 'magic number' m_{Λ} has the property that any two convex subsets of Λ can be distinguished by their X-rays in any set of m_{Λ} prescribed Λ-directions. Recent calculations suggest that (with one exception in the case n=4) the least possible magic number for n-cyclotomic model sets might just be N+1, where N=lcm(n,2).
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