Sphere Packings, VI. Tame Graphs and Linear Programs
| Autor: | Thomas C. Hales |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Discrete mathematics
Conjecture Linear programming Theoretical Computer Science Planar graph Combinatorics Kepler conjecture symbols.namesake Packing problems Compact space Sphere packing Computational Theory and Mathematics symbols Discrete Mathematics and Combinatorics Geometry and Topology Isomorphism Mathematics |
| Zdroj: | Discrete & Computational Geometry. 36:205-265 |
| ISSN: | 1432-0444 0179-5376 |
| DOI: | 10.1007/s00454-005-1215-x |
| Popis: | This paper is the sixth and final part in a series of papers devoted to the proof of the Kepler conjecture, which asserts that no packing of congruent balls in three dimensions has density greater than the face-centered cubic packing. In a previous paper in this series, a continuous function f on a compact space is defined, certain points in the domain are conjectured to give the global maxima, and the relation between this conjecture and the Kepler conjecture is established. In this paper we consider the set of all points in the domain for which the value of f is at least the conjectured maximum. To each such point, we attach a planar graph. It is proved that each such graph must be isomorphic to a tame graph, of which there are only finitely many up to isomorphism. Linear programming methods are then used to eliminate all possibilities, except for three special cases treated in earlier papers: pentahedral prisms, the face-centered cubic packing, and the hexagonal-close packing. The results of this paper rely on long computer calculations. |
| Databáze: | OpenAIRE |
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