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.
|Title of host publication||A Journey through Discrete Mathematics|
|Subtitle of host publication||A Tribute to Jiri Matousek|
|Publisher||Springer International Publishing|
|Number of pages||18|
|State||Published - 1 Jan 2017|
Bibliographical notePublisher Copyright:
© Springer International Publishing AG 2017.
ASJC Scopus subject areas
- Computer Science (all)
- Mathematics (all)
- Economics, Econometrics and Finance (all)
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