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  1. Discrete & Computational Geometry
  2. Discrete & Computational Geometry : Volume 47
  3. Discrete & Computational Geometry : Volume 47, Issue 3, April 2012
  4. Octants Are Cover-Decomposable
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Discrete & Computational Geometry : Volume 57
Discrete & Computational Geometry : Volume 56
Discrete & Computational Geometry : Volume 55
Discrete & Computational Geometry : Volume 54
Discrete & Computational Geometry : Volume 53
Discrete & Computational Geometry : Volume 52
Discrete & Computational Geometry : Volume 51
Discrete & Computational Geometry : Volume 50
Discrete & Computational Geometry : Volume 49
Discrete & Computational Geometry : Volume 48
Discrete & Computational Geometry : Volume 47
Discrete & Computational Geometry : Volume 47, Issue 4, June 2012
Discrete & Computational Geometry : Volume 47, Issue 3, April 2012
A Generalisation of Tverberg’s Theorem
The Shape of Orthogonal Cycles in Three Dimensions
A Simpler Proof of the Boros–Füredi–Bárány–Pach–Gromov Theorem
Moving Out the Edges of a Lattice Polygon
Maximal f-Vectors of Minkowski Sums of Large Numbers of Polytopes
A Hyperplane Inequality for Measures of Convex Bodies in ℝ n , n≤4
Sphere and Dot Product Representations of Graphs
Embedding a Pair of Graphs in a Surface, and the Width of 4-dimensional Prismatoids
Refined Bounds on the Number of Connected Components of Sign Conditions on a Variety
Octants Are Cover-Decomposable
Non-rigidity of Spherical Inversive Distance Circle Packings
Counterexamples of the Conjecture on Roots of Ehrhart Polynomials
Smooth Fano Polytopes Whose Ehrhart Polynomial Has a Root with Large Real Part
Scissors Congruence, the Golden Ratio and Volumes in Hyperbolic 5-Space
Discrete & Computational Geometry : Volume 47, Issue 2, March 2012
Discrete & Computational Geometry : Volume 47, Issue 1, January 2012
Discrete & Computational Geometry : Volume 46
Discrete & Computational Geometry : Volume 45
Discrete & Computational Geometry : Volume 44
Discrete & Computational Geometry : Volume 43
Discrete & Computational Geometry : Volume 42
Discrete & Computational Geometry : Volume 41
Discrete & Computational Geometry : Volume 40
Discrete & Computational Geometry : Volume 39
Discrete & Computational Geometry : Volume 38
Discrete & Computational Geometry : Volume 37
Discrete & Computational Geometry : Volume 36
Discrete & Computational Geometry : Volume 35
Discrete & Computational Geometry : Volume 34
Discrete & Computational Geometry : Volume 33
Discrete & Computational Geometry : Volume 32
Discrete & Computational Geometry : Volume 31
Discrete & Computational Geometry : Volume 30
Discrete & Computational Geometry : Volume 29
Discrete & Computational Geometry : Volume 28
Discrete & Computational Geometry : Volume 27
Discrete & Computational Geometry : Volume 26
Discrete & Computational Geometry : Volume 25
Discrete & Computational Geometry : Volume 24
Discrete & Computational Geometry : Volume 23
Discrete & Computational Geometry : Volume 22
Discrete & Computational Geometry : Volume 21
Discrete & Computational Geometry : Volume 20
Discrete & Computational Geometry : Volume 19
Discrete & Computational Geometry : Volume 18
Discrete & Computational Geometry : Volume 17

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Octants Are Cover-Decomposable

Content Provider Springer Nature Link
Author Keszegh, Balázs Pálvölgyi, Dömötör
Copyright Year 2011
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 the translates of a given open triangle can be decomposed into two coverings. However, we exhibit an indecomposable 3-fold covering with translates of a given triangle.
Starting Page 598
Ending Page 609
Page Count 12
File Format PDF
ISSN 01795376
Journal Discrete & Computational Geometry
Volume Number 47
Issue Number 3
e-ISSN 14320444
Language English
Publisher Springer-Verlag
Publisher Date 2011-10-19
Publisher Place New York
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Cover-decomposability Geometric hypergraph coloring Computational Mathematics and Numerical Analysis Combinatorics
Content Type Text
Resource Type Article
Subject Discrete Mathematics and Combinatorics Theoretical Computer Science Computational Theory and Mathematics Geometry and Topology
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