Octants are Cover Decomposable

zbMATH Open1274.52025arXiv1101.3773MaRDI QIDQ2857395

Dömötör Pálvölgyi, Balázs Keszegh

Publication date: 1 November 2013

Abstract: We prove that octants are cover-decomposable, i.e., any 12-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into two coverings. As a corollary, we obtain that any 12-fold covering of any subset of the plane with a finite number of homothetic copies of a given triangle can be decomposed into two coverings. We also show that any 12-fold covering of the whole plane with open triangles can be decomposed into two coverings. However, we exhibit an indecomposable 3-fold covering.

Full work available at URL: https://arxiv.org/abs/1101.3773

Mathematics Subject Classification ID

Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15)

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