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A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
This matrix belongs to the modular group (,). This equivalence of lattices can be thought of as underlying many of the properties of elliptic functions (especially the Weierstrass elliptic function ) and modular forms.
The continuant (,, …,) can be computed by taking the sum of all possible products of x 1,...,x n, in which any number of disjoint pairs of consecutive terms are deleted (Euler's rule).
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
In complex analysis, Gauss's continued fraction is a particular class of continued fractions derived from hypergeometric functions. It was one of the first analytic continued fractions known to mathematics, and it can be used to represent several important elementary functions , as well as some of the more complicated transcendental functions .
Unimodular lattices are equal to their dual lattices, and for this reason, unimodular lattices are also known as self-dual. Given a pair (m,n) of nonnegative integers, an even unimodular lattice of signature (m,n) exists if and only if m−n is divisible by 8, but an odd unimodular lattice of signature (m,n) always exists. In particular, even ...
In mathematics, the Smith–Minkowski–Siegel mass formula (or Minkowski–Siegel mass formula) is a formula for the sum of the weights of the lattices (quadratic forms) in a genus, weighted by the reciprocals of the orders of their automorphism groups. The mass formula is often given for integral quadratic forms, though it can be generalized ...
The automorphism group (or group of congruences) of the integer lattice consists of all permutations and sign changes of the coordinates, and is of order 2 n n!.As a matrix group it is given by the set of all n × n signed permutation matrices.