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On the Steinhaus tiling problem

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Mihail N. Kolountzakis  and
Thomas Wolff
Mihail N. Kolountzakis
Affiliation:
Department of Mathematics, University of Crete, 714 09 Iraklion, Crete, Greece. e-mail: kolount@math.uch.gr
Thomas Wolff
Affiliation:
Department of Mathematics, 253-37 Caltech, Pasadena, CA 91125, USA. e-mail: wolff@cco.caltech.edu
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Abstract

Several results are proved related to a question of Steinhaus: is there a set E⊂ℝ2 such that the image of E under each rigid motion of IR2 contains exactly one lattice point? Assuming measurability, the analogous question in higher dimensions is answered in the negative, and on the known partial results in the two dimensional case are improved on. Also considered is a related problem involving finite sets of rotations.

MSC classification

Secondary: 52A37: Other problems of combinatorial convexity
Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999 , pp. 253 - 280
Copyright
Copyright © University College London 1999

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