Rational polygons: Odd compression ratio and odd plane coverings

Rom Pinchasi, Yuri Rabinovich

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.

Original languageEnglish
Title of host publicationA Journey through Discrete Mathematics
Subtitle of host publicationA Tribute to Jiri Matousek
PublisherSpringer International Publishing
Number of pages18
ISBN (Electronic)9783319444796
ISBN (Print)9783319444789
StatePublished - 1 Jan 2017

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2017.

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics
  • General Economics, Econometrics and Finance
  • General Business, Management and Accounting


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