Results 1  10
of
186,655
The Cell Structures of Certain Lattices
, 1991
"... . The most important lattices in Euclidean space of dimension n 8 are the lattices A n (n ³ 2), D n (n ³ 4), E n (n = 6 , 7 , 8) and their duals. In this paper we determine the cell structures of all these lattices and their Voronoi and Delaunay polytopes in a uniform manner. The results for E 6 * ..."
Abstract

Cited by 23 (6 self)
 Add to MetaCart
. The most important lattices in Euclidean space of dimension n 8 are the lattices A n (n ³ 2), D n (n ³ 4), E n (n = 6 , 7 , 8) and their duals. In this paper we determine the cell structures of all these lattices and their Voronoi and Delaunay polytopes in a uniform manner. The results for E 6
On the Voronoi regions of certain lattices
 MIT LIBRARIES. DOWNLOADED ON OCTOBER 28, 2008 AT 20:11 FROM IEEE XPLORE. RESTRICTIONS APPLY. ET AL.: DESIGN OF SPHERICAL LATTICE SPACE–TIME CODES 4865
, 1984
"... The Voronoi region of a lattice Ln R is the convex polytope consisting of all points of I that are closer to the origin than to any other point of Ln. In this paper we calculate the second moments of the Voronoi regions of the lattices E6*, E7*, K12, A16 and A24. The results show that these lattic ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
The Voronoi region of a lattice Ln R is the convex polytope consisting of all points of I that are closer to the origin than to any other point of Ln. In this paper we calculate the second moments of the Voronoi regions of the lattices E6*, E7*, K12, A16 and A24. The results show
COMBINATORIAL DATA OF CERTAIN LATTICE PATHS
"... Abstract. In this paper, we will consider certain lattice paths in the twodimensional space R2, satisfying the socalled axis property: if a lattice path starts at the point (0, 0) and ends on the horizontal axis (or the xaxis) of R2, then we will say that this lattice path satisfies the axis prop ..."
Abstract
 Add to MetaCart
Abstract. In this paper, we will consider certain lattice paths in the twodimensional space R2, satisfying the socalled axis property: if a lattice path starts at the point (0, 0) and ends on the horizontal axis (or the xaxis) of R2, then we will say that this lattice path satisfies the axis
Finite Vector Spaces and Certain Lattices
, 1998
"... The Galois number G n (q) is defined to be the number of subspaces of the ndimensional vector space over the finite field GF (q). When q is prime, we prove that G n (q) is equal to the number L n (q)ofndimensional mod q lattices, which are defined to be lattices (that is, discrete additive subg ..."
Abstract
 Add to MetaCart
The Galois number G n (q) is defined to be the number of subspaces of the ndimensional vector space over the finite field GF (q). When q is prime, we prove that G n (q) is equal to the number L n (q)ofndimensional mod q lattices, which are defined to be lattices (that is, discrete additive
On certain lattices associated with generic division algebras
 J. Group Theory
"... Abstract. Let Sn denote the symmetric group on n letters. We consider the Snlattice An−1 = {(z1,..., zn) ∈ Zn  ∑ i zi = 0}, where Sn acts on Zn by permuting the coordinates, and its squares A ⊗2 n−1, Sym2 An−1, and ∧2 An−1. For odd values of n, we show that A ⊗2 n−1 is equivalent to ∧2 An−1 in th ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
Abstract. Let Sn denote the symmetric group on n letters. We consider the Snlattice An−1 = {(z1,..., zn) ∈ Zn  ∑ i zi = 0}, where Sn acts on Zn by permuting the coordinates, and its squares A ⊗2 n−1, Sym2 An−1, and ∧2 An−1. For odd values of n, we show that A ⊗2 n−1 is equivalent to ∧2 An−1
Submodular functions, matroids and certain polyhedra
, 2003
"... The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts is that all ..."
Abstract

Cited by 346 (0 self)
 Add to MetaCart
The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts
On Lattices, Learning with Errors, Random Linear Codes, and Cryptography
 In STOC
, 2005
"... Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear co ..."
Abstract

Cited by 359 (6 self)
 Add to MetaCart
Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear
Cones of matrices and setfunctions and 01 optimization
 SIAM JOURNAL ON OPTIMIZATION
, 1991
"... It has been recognized recently that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedron, is a powerful tool in polyhedral combinatorics. We develop a general method to construct higherdimensional polyhedra (or, in some cases, convex sets) whose projection a ..."
Abstract

Cited by 343 (7 self)
 Add to MetaCart
that the stable set polytope is the projection of a polytope with a polynomial number of facets. We also discuss an extension of the method, which establishes a connection with certain submodular functions and the Möbius function of a lattice.
Results 1  10
of
186,655