Densest Packings of Typical Convex Sets Are Not Lattice-Like .
Fejes G. Tóth (1995)
Discrete & computational geometry
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Displaying similar documents to “On the boundary of an extremal body.”
Densest Packings of Typical Convex Sets Are Not Lattice-Like .
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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On rhombic dodecahedra.
Bezdek, Károly (2000)
Beiträge zur Algebra und Geometrie
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A mean-square bound for the lattice discrepancy of bodies of rotation with flat points on the boundary
Werner Georg Nowak (2007)
Acta Arithmetica
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On the index of the boundary points of four-dimensional lattices that are admissible for a cube.
Smirnov, Yu.A. (2005)
Journal of Mathematical Sciences (New York)
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Double-Lattice Packings of Convex Bodies in the Plane.
W. Kuperberg, G. Kuperberg (1990)
Discrete & computational geometry
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Lattice points in a circle: An improved mean-square asymptotics
Werner Georg Nowak (2004)
Acta Arithmetica
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Characterization of Birkhoff’s Conditions by Means of Cover-Preserving and Partially Cover-Preserving Sublattices
Marcin Łazarz (2016)
Bulletin of the Section of Logic
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In the paper we investigate Birkhoff’s conditions (Bi) and (Bi*). We prove that a discrete lattice L satisfies the condition (Bi) (the condition (Bi*)) if and only if L is a 4-cell lattice not containing a cover-preserving sublattice isomorphic to the lattice S*7 (the lattice S7). As a corollary we obtain a well known result of J. Jakub´ık from [6]. Furthermore, lattices S7 and S*7 are considered as so-called partially cover-preserving sublattices of a given lattice L, S7 ≪ L and S7...
On Linear Sections of Lattice Packings.
H. Groemer (1986)
Monatshefte für Mathematik
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Lattice points in bodies with algebraic boundary
Wolfgang Müller (2003)
Acta Arithmetica
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Successive Minima, Intrinsic Volumes, and Lattice Determinants.
U. Schnell (1995)
Discrete & computational geometry
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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...
Crystal lattices and sub-lattices
J. L. Ericksen (1982)
Rendiconti del Seminario Matematico della Università di Padova
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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...