Local Theory of Regular Systems and Delone Sets

We survey the results of the local theory of regular systems that are related to estimating the regularity radius. We also discuss recent results on local groups in arbitrary Delone sets in the plane and in the three-dimensional space, including new theorems and conjectures generalizing the classica...

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Published in:Proceedings of the Steklov Institute of Mathematics 2024-06, Vol.325 (1), p.120-135
Main Author: Dolbilin, N. P.
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Language:English
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description We survey the results of the local theory of regular systems that are related to estimating the regularity radius. We also discuss recent results on local groups in arbitrary Delone sets in the plane and in the three-dimensional space, including new theorems and conjectures generalizing the classical statement on the absence of fivefold rotations in lattices.
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Mathematics
Mathematics and Statistics
title Local Theory of Regular Systems and Delone Sets
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