On a generalization of the Hermite constant (Q1375072)
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scientific article; zbMATH DE number 1099692
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a generalization of the Hermite constant |
scientific article; zbMATH DE number 1099692 |
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On a generalization of the Hermite constant (English)
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5 January 1998
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In the Introduction of this paper the author surveys some results on the theory of sphere packings in the \(n\)-dimensional Euclidean space; in this report he summarizes the information about the densities of the different types of sphere packings. Then he gives a method to build quasiperiodic sphere packings controlled by a finite group, and introduces a generalized Hermite function which he uses to find upper bounds for the densities of these packings. Finally he indicates a few examples associated with Penrose tilings concerned with some space-filling problems in crystallography and modelling of quasicrystals in physics.
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sphere packings
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quasiperiodic sphere packings
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densities of packings
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generalized Hermite constant
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crystallography
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0.93603116
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0.9197995
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0.9164045
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