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Indecomposable Coverings with Homothetic Polygons

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We prove that for any convex polygon \(S\) with at least four sides, or a concave one with no parallel sides, and any \(m>0\), there is an \(m\)-fold covering of the plane with homothetic copies of \(S\) that cannot be decomposed into two coverings.

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I would like to thank my supervisor Géza Tóth for all the help and for the many discussions. Without him this article would not have been completed. This work has been supported by OTKA NN-102029.

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Correspondence to István Kovács.

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Editor in Charge: János Pach

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Kovács, I. Indecomposable Coverings with Homothetic Polygons. Discrete Comput Geom 53, 817–824 (2015). https://doi.org/10.1007/s00454-015-9687-9

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  • Homothetic copy
  • Multiple covering
  • Decomposable