New Lower Bound for the Optimal Ball Packing Density in Hyperbolic 4-Space
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  • 作者:Robert Thijs Kozma ; Jen? Szirmai
  • 关键词:Coxeter group ; Horoball ; Hyperbolic geometry ; Packing ; Tiling ; 52C17 ; 52C22 ; 52B15
  • 刊名:Discrete and Computational Geometry
  • 出版年:2015
  • 出版时间:January 2015
  • 年:2015
  • 卷:53
  • 期:1
  • 页码:182-198
  • 全文大小:674 KB
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  • 刊物类别:Mathematics and Statistics
  • 刊物主题:Mathematics
    Combinatorics
    Computational Mathematics and Numerical Analysis
  • 出版者:Springer New York
  • ISSN:1432-0444
文摘
In this paper we consider ball packings in \(4\) -dimensional hyperbolic space. We show that it is possible to exceed the conjectured \(4\) -dimensional realizable packing density upper bound due to L. Fejes-Tóth (Regular Figures, Macmillian, New York, 1964). We give seven examples of horoball packing configurations that yield higher densities of \(0.71644896\dots \) , where horoballs are centered at ideal vertices of certain Coxeter simplices, and are invariant under the actions of their respective Coxeter groups.

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