2011/01/19 by Balázs Keszegh, Keszegh, Balázs, Dömötör Pálvölgyi +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1101.3773
openalex publication_date 2011/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.