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arXiv · 1701.00700

Rational Polygons: Odd Compression Ratio and Odd Plane Coverings

Rom Pinchasi·Yuri Rabinovich
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Abstract

Let P be a polygon with rational vertices in the plane. We show that for any finite odd-sized collection of translates of P, the area of the set of points lying in an odd number of these translates is bounded away from 0 by a constant depending on P alone. The key ingredient of the proof is a construction of an odd cover of the plane by translates of P. That is, we establish a family F of translates of P covering (almost) every point in the plane a uniformly bounded odd number of times.

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Rom Pinchasi, Yuri Rabinovich. 2017-01-03. Rational Polygons: Odd Compression Ratio and Odd Plane Coverings. https://arxiv.org/abs/1701.00700

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