Lattices

Some articles on lattices, lattice:

Smith–Minkowski–Siegel Mass Formula - Examples - Dimension n = 32
... that there are more than 80 million even unimodular lattices of dimension 32, as each has automorphism group of order at least 2 so contributes at most 1/2 to the mass ... refining this argument, King (2003) showed that there are more than a billion such lattices ... In higher dimensions the mass, and hence the number of lattices, increases very rapidly ...
Lattice-based Cryptography - History
... Lattices were first studied by mathematicians Joseph Louis Lagrange and Carl Friedrich Gauss ... Lattices have been used recently in computer algorithms and in cryptanalysis ... In 1996, Miklós Ajtai showed in a seminal result the use of lattices as a cryptography primitive ...
Lattice (discrete Subgroup) - S-arithmetic Lattices
... Arithmetic lattices admit an important generalization, known as the S-arithmetic lattices ... The first example is given by the diagonally embedded subgroup This is a lattice in the product of algebraic groups over different local fields, both real and p-adic ... Under fairly general assumptions, this construction indeed produces a lattice ...
Chabauty Topology
... The intuitive idea may be seen in the case of the set of all lattices in a Euclidean space E ... by in a sense taking limiting cases or degenerating a certain sequence of lattices ... One can find linear subspaces or discrete groups that are lattices in a subspace, depending on how one takes a limit ...
List Of First-order Theories - Lattices
... Lattices can be considered either as special sorts of partially ordered sets, with a signature consisting of one binary relation symbol ≤, or as ... For two binary operations the axioms for a lattice are Commutative laws Associative laws Absorption laws For one relation ≤ the axioms are Axioms stating ≤ is a ... existence of c=a∧b) (existence of c=a∨b) First order properties include (distributive lattices) (modular lattices) Completeness is not a first order ...