Multiple coverings with closed polygons

Kovács, István and Tóth, Géza (2015) Multiple coverings with closed polygons. ELECTRONIC JOURNAL OF COMBINATORICS, 22 (1). ISSN 1097-1440

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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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