### Some articles on *lattices, lattice*:

Smith–Minkowski–Siegel Mass Formula - Examples - Dimension

... that there are more than 80 million even unimodular

*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

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**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) -

... Arithmetic

*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

... 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 -

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**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 ...Main Site Subjects

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