Economical Coverings of Sets of Lattice Points.
N. Alon (1991)
Geometric and functional analysis
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Displaying similar documents to “Voronoĭ type criteria for lattice coverings with balls”
Economical Coverings of Sets of Lattice Points.
On conjectures of Minkowski and Woods for n=8
R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi (2011)
Acta Arithmetica
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On the thinnest 2-fold double-lattice covering with a centrally symmetric convex domain. (Über die dünnste doppelgitterförmige 2-fache Überdeckung mit einem zentralsymmetrischen konvexen Bereich.)
Temesvári, Ágota H. (1994)
Beiträge zur Algebra und Geometrie
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On a problem of Ryškov concerning lattice coverings
R. Bambah, N. Sloane (1982)
Acta Arithmetica
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Classification systems and their lattice
Sándor Radeleczki (2002)
Discussiones Mathematicae - General Algebra and Applications
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We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent...
The densest lattice in twenty-four dimensions.
Cohn, Henry, Kumar, Abhinav (2004)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Strong elements in lattices
Josef Dalík (1979)
Časopis pro pěstování matematiky
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On a Hadwiger-Wills inequality concerning lattice points.
Kołodziejczyk, Krzysztof (1999)
Beiträge zur Algebra und Geometrie
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Orthogonality spaces and atomistic orthocomplemented lattices
Jarmila Hedlíková, Sylvia Pulmannová (1991)
Czechoslovak Mathematical Journal
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Some generalization of Steinhaus' lattice points problem
Paweł Zwoleński (2011)
Colloquium Mathematicae
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Steinhaus' lattice points problem addresses the question of whether it is possible to cover exactly n lattice points on the plane with an open ball for every fixed nonnegative integer n. This paper includes a theorem which can be used to solve the general problem of covering elements of so-called quasi-finite sets in Hilbert spaces. Some applications of this theorem are considered.
Dual Lattice of ℤ-module Lattice
Yuichi Futa, Yasunari Shidama (2017)
Formalized Mathematics
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In this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a dual basis can be calculated by elements of an inverse of the Gram Matrix. We also formalize a summation of inner products and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic...