Rational Polygons: Odd Compression Ratio and Odd Plane Coverings
Combinatorics
2017-01-04 v1 Metric Geometry
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.
Cite
@article{arxiv.1701.00700,
title = {Rational Polygons: Odd Compression Ratio and Odd Plane Coverings},
author = {Rom Pinchasi and Yuri Rabinovich},
journal= {arXiv preprint arXiv:1701.00700},
year = {2017}
}
Comments
The final version of the contribution is due to be published in the collection of papers "A Journey through Discrete Mathematics: A Tribute to Jiri Matousek" edited by Martin Loebl, Jaroslav Nesetril and Robin Thomas, due to be published by Springer