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Dal'nevostochnyi Matematicheskii Zhurnal, 2011, Volume 11, Number 1, Pages 48–55
(Mi dvmg210)
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This article is cited in 6 scientific papers (total in 6 papers)
The average number of vertexes of Klein polyhedrons for integer lattices
A. A. Illarionov, D. Slinkin Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
Abstract:
Low estimate for the average number for vertices of Klein polyhedron of integer lattices with given determinant is derived. The low estimate coincides with the high estimate up to a constant. The constant depends on dimension of lattices. High-low estimates for the number of relative minima of integer lattices with given determinant is derived from this fact.
Key words:
high dimension continued fraction, relative minimum, Klein polyhedron.
Received: 02.09.2010
Citation:
A. A. Illarionov, D. Slinkin, “The average number of vertexes of Klein polyhedrons for integer lattices”, Dal'nevost. Mat. Zh., 11:1 (2011), 48–55
Linking options:
https://www.mathnet.ru/eng/dvmg210 https://www.mathnet.ru/eng/dvmg/v11/i1/p48
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Abstract page: | 473 | Full-text PDF : | 103 | References: | 59 | First page: | 1 |
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