Rational Polygons: Odd Compression Ratio and Odd Plane Coverings

Autor:	Pinchasi, Rom, Rabinovich, Yuri
Rok vydání:	2017
Předmět:	Mathematics - Combinatorics Mathematics - Metric Geometry
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1701.00700 Zobrazit plný text záznamu View this record from Arxiv