Rational polygons: Odd compression ratio and odd plane coverings

Rom Pinchasi; Yuri Rabinovich

doi:https://doi.org/10.1007/978-3-319-44479-6_28

Rational polygons: Odd compression ratio and odd plane coverings

Rom Pinchasi, Yuri Rabinovich

Technion - Israel Institute of Technology, University of Haifa

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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.

Original language	English
Title of host publication	A Journey through Discrete Mathematics
Subtitle of host publication	A Tribute to Jiri Matousek
Pages	693-710
Number of pages	18
ISBN (Electronic)	9783319444796
DOIs	https://doi.org/10.1007/978-3-319-44479-6_28
State	Published - 1 Jan 2017

All Science Journal Classification (ASJC) codes

Economics, Econometrics and Finance(all)
General Computer Science
General Economics,Econometrics and Finance
General Business,Management and Accounting
General Mathematics

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https://doi.org/10.1007/978-3-319-44479-6_28

Cite this

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Rational polygons: Odd compression ratio and odd plane coverings

Abstract

All Science Journal Classification (ASJC) codes

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