The average number of vertices of Klein polyhedra for integer lattices (Q2906408)
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scientific article; zbMATH DE number 6077456
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The average number of vertices of Klein polyhedra for integer lattices |
scientific article; zbMATH DE number 6077456 |
Statements
5 September 2012
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multidimensional continued fractions
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relative minima
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Klein polyhedra
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The average number of vertices of Klein polyhedra for integer lattices (English)
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Consider Klein polyhedra for integer \(s\)-dimensional lattices of determinant \(N\). The authors show a lower bound for the average number of vertices of such polyhedra. This lover bound up to a constant depending only on \(s\) coincides with the currently known upper bound for this number. In particular, this implies the lower bound for the number of local minima.
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