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A Danzer set for axis parallel boxes

Authors: David Simmons and Yaar Solomon
Journal: Proc. Amer. Math. Soc. 144 (2016), 2725-2729
MSC (2010): Primary 54H20, 65D18, 68R01
Published electronically: October 21, 2015
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Abstract: We present concrete constructions of discrete sets in $ \mathbb{R}^d$ ($ d\ge 2$) that intersect every aligned box of volume $ 1$ in $ \mathbb{R}^d$, and which have optimal growth rate $ O(T^d)$.

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Additional Information

David Simmons
Affiliation: Department of Mathematics, University of York, Heslington, York YO10 5DD, United Kingdom

Yaar Solomon
Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York

Received by editor(s): January 21, 2015
Received by editor(s) in revised form: July 21, 2015
Published electronically: October 21, 2015
Communicated by: Nimish Shah
Article copyright: © Copyright 2015 American Mathematical Society