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Rational Polygons: Odd Compression Ratio and Odd Plane Coverings

In: A Journey Through Discrete Mathematics

Author

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  • Rom Pinchasi

    (Technion–Israel Institute of Technology, Mathematics Department)

  • Yuri Rabinovich

    (Haifa University, Department of Computer Science)

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

Suggested Citation

  • Rom Pinchasi & Yuri Rabinovich, 2017. "Rational Polygons: Odd Compression Ratio and Odd Plane Coverings," Springer Books, in: Martin Loebl & Jaroslav Nešetřil & Robin Thomas (ed.), A Journey Through Discrete Mathematics, pages 693-710, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-44479-6_28
    DOI: 10.1007/978-3-319-44479-6_28
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