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arXiv · 1403.2653

Multiple coverings with closed polygons

István Kovács·Géza Tóth
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Abstract

A planar set $P$ is said to be cover-decomposable if there is a constant $k=k(P)$ such that every $k$-fold covering of the plane with translates of $P$ can be decomposed into two coverings. It is known that open convex polygons are cover-decomposable. Here we show that closed, centrally symmetric convex polygons are also cover-decomposable. We also show that an infinite-fold covering of the plane with translates of $P$ can be decomposed into two infinite-fold coverings. Both results hold for coverings of any subset of the plane.

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István Kovács, Géza Tóth. 2014-03-09. Multiple coverings with closed polygons. https://arxiv.org/abs/1403.2653

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