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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 239, Pages 52–62
(Mi tm358)
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A Relative Ryshkov Perfect Polyhedron As a Generatrix of a W-Tiling
R. G. Barykinskii M. V. Lomonosov Moscow State University
Abstract:
For an arbitrary positive definite quadratic form f in n variables (n-PQF) and any positive number ρ, the notion of (f,ρ)-perfect (n+m)-PQF is introduced. The problem of finding all such forms for any given n-PQF f and ρ>0 is studied. Two representations of all (f,ρ)-perfect (n+1)-PQFs are obtained: one in the form of the vertices of a tiling of the Euclidean n-space (we call this tiling a W-tiling corresponding to the n-PQF f and the number ρ), and the other in the form of the vertices of an n-dimensional polyhedral surface μf(ρ) (we call it a relative Ryshkov perfect polyhedron corresponding to the n-PQF f and the number ρ). It is proved that the polyhedron μf(ρ) is a generatrix of the W-tiling corresponding to the n-PQF f and the number ρ.
Received in April 2002
Citation:
R. G. Barykinskii, “A Relative Ryshkov Perfect Polyhedron As a Generatrix of a W-Tiling”, Discrete geometry and geometry of numbers, Collected papers. Dedicated to the 70th birthday of professor Sergei Sergeevich Ryshkov, Trudy Mat. Inst. Steklova, 239, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 52–62; Proc. Steklov Inst. Math., 239 (2002), 45–54
Linking options:
https://www.mathnet.ru/eng/tm358 https://www.mathnet.ru/eng/tm/v239/p52
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Abstract page: | 244 | Full-text PDF : | 92 | References: | 64 |
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