Rational polygons: Odd compression ratio and odd plane coverings

Rom Pinchasi; Yuri Rabinovich

doi:10.1007/978-3-319-44479-6_28

Rational polygons: Odd compression ratio and odd plane coverings

Rom Pinchasi, Yuri Rabinovich

Department of Computer Science

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
Publisher	Springer International Publishing
Pages	693-710
Number of pages	18
ISBN (Electronic)	9783319444796
ISBN (Print)	9783319444789
DOIs	https://doi.org/10.1007/978-3-319-44479-6_28
State	Published - 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

Access to Document

10.1007/978-3-319-44479-6_28

Cite this

@inbook{4f81479c49ab4788b4fe1c40a25d8752,

title = "Rational polygons: Odd compression ratio and odd plane coverings",

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.",

author = "Rom Pinchasi and Yuri Rabinovich",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.",

year = "2017",

month = jan,

day = "1",

doi = "10.1007/978-3-319-44479-6\_28",

language = "English",

isbn = "9783319444789",

pages = "693--710",

booktitle = "A Journey through Discrete Mathematics",

publisher = "Springer International Publishing",

address = "Switzerland",

}

TY - CHAP

T1 - Rational polygons

T2 - Odd compression ratio and odd plane coverings

AU - Pinchasi, Rom

AU - Rabinovich, Yuri

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85042441710

U2 - 10.1007/978-3-319-44479-6_28

DO - 10.1007/978-3-319-44479-6_28

M3 - Chapter

AN - SCOPUS:85042441710

SN - 9783319444789

SP - 693

EP - 710

BT - A Journey through Discrete Mathematics

PB - Springer International Publishing

ER -

Rational polygons: Odd compression ratio and odd plane coverings

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this