Rational Polygons: Odd Compression Ratio and Odd Plane Coverings

  • Rom Pinchasi
  • Yuri Rabinovich


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 \(\mathcal{F}\) of translates of P covering (almost) every point in the plane a uniformly bounded odd number of times.


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Copyright information

© Springer International publishing AG 2017

Authors and Affiliations

  1. 1.Mathematics DepartmentTechnion–Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of Computer ScienceHaifa UniversityHaifaIsrael

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