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Information about Lattice Theory

Lattice may refer to:

See also

Latticework is an ornament, lattice framework consisting of a criss-crossed pattern of strips of building material, usually wood or metal but can be of any material. The design is created by crossing the strips to form a decorative network.
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lath is a thin, narrow strip of some straight-grained wood or other material, including metal or gypsum. A lattice, or lattice-work, is a criss-crossed or interlaced arrangement of laths, or the pattern made by such an arrangement.
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kagome lattice is an arrangement of laths composed of interlaced triangles such that each point where two laths cross has four neighboring points. Although called a lattice, it is more closely related to the trihexagonal tiling than to a mathematical lattice.
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lattice girder is a girder where the flanges are connected by a lattice web.[1] This type of design has been supplanted in modern construction with welded or bolted plate girders, which use more material but have lower fabrication costs.
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A lattice tower is a freestanding steel framework tower. It is used as a pylon especially for voltages above 100 kilovolts, as a radio tower (a self-radiating tower or as a carrier for aerials) or as an observation tower.
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A lattice bridge is a form of truss bridge that uses a large number of small and closely spaced diagonal elements that form a lattice. It was patented by architect Ithiel Town in 1820 and 1835 as Town's lattice truss.
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The criss-crossing pattern of strips in this pastry is reminiscent of the laths in a garden trellis, as well as a Hasse diagram of a lattice in mathematics.

The idea of latticed pastry is used as a lid to many different tarts or pies.

See also

  • pastry
  • lattice

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In mathematics, a lattice can be:
  • In one usage, a lattice is a partially ordered set (poset) in which any two elements have a supremum and an infimum—see lattice (order).

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lattice is a partially ordered set (or poset) in which every pair of elements has a unique supremum (the elements' least upper bound; called their join) and an infimum (greatest lower bound; called their meet).
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Formal concept analysis, introduced by Rudolf Wille and his students, is a method of data analysis that takes an input matrix specifying a set of objects and the properties thereof, and finds both all the "natural" clusters of properties
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lattice of subgroups of a group is the lattice whose elements are the subgroups of , with the partial order relation being set inclusion. In this lattice, the join of two subgroups is the subgroup generated by their union, and the meet of two subgroups is their intersection.
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lattice in Rn is a discrete subgroup of Rn which spans the real vector space Rn. Every lattice in Rn
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In geometry and crystallography, a Bravais lattice, named after Auguste Bravais, is an infinite set of points generated by a set of discrete translation operations. A crystal is made up of one or more atoms (the basis) which is repeated at each lattice point.
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hexagonal lattice or equilateral triangular lattice is one of the five 2D lattice types.

Three nearby points form an equilateral triangle. In images four orientations of such a triangle are by far the most common.
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Eisenstein integers, named after Ferdinand Eisenstein, are complex numbers of the form



where a and b are integers and



is a complex cube root of unity.
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In mathematics, The n-dimensional integer lattice (or cubic lattice), denoted Zn, is the lattice in the Euclidean space Rn whose lattice points are n-tuples of integers.
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In mathematics, a Niemeier lattice is one of the 24 positive definite even unimodular lattices of rank 24, which were classified by Hans-Volker Niemeier. The best-known example is the Leech lattice.
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In crystallography, the reciprocal lattice of a Bravais lattice is the set of all vectors K such that



for all lattice point position vectors R.
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square lattice is one of the five 2D lattice types. It is the two-dimensional version of the integer lattice.

Two orientations of an image of the lattice are by far the most common.
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A Gaussian integer is a complex number whose real and imaginary part are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z[i].
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In mathematics, a unimodular lattice is a lattice of discriminant 1 or −1. The E8 lattice and the Leech lattice are two famous examples.

Definitions

  • A lattice

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In mathematics, the Leech lattice is a particular lattice Λ in 24-dimensional Euclidean space, R24 discovered by John Leech in 1965. (Ernst Witt discovered it in 1940, but did not publish his discovery; see his collected works for details.
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E8 is the name given to a family of closely related structures. In particular, it is the name of some exceptional simple Lie algebras as well as that of the associated simple Lie groups.
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In mathematics, an arithmetic lattice is a lattice derived from a division algebra, for example quaternions.
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Bethe lattice or Cayley tree, introduced by Hans Bethe in 1935, is a connected cycle-free graph where each node is connected to z neighbours, where z is called the coordination number.
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crystal structure is a unique arrangement of atoms in a crystal. A crystal structure is composed of a motif, a set of atoms arranged in a particular way, and a lattice. Motifs are located upon the points of a lattice, which is an array of points repeating periodically in three
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lattice model is a physical model that is defined on a lattice, as opposed to the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice.
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Lattice Semiconductor

Public (NASDAQ:  LSCC )
Founded 1983, public since 1989
Headquarters Hillsboro, Oregon,
United States

Key people Stephen A. Skaggs,
Jan Johannessen
Industry Integrated Circuits
Products FPGAs, CPLDs
Website www.
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Lattice C (according to its author, Lattice, Incorporated) was the first C compiler for MS-DOS on the IBM PC, in 1982. It was ported to many other platforms, such as mainframes (MVS), minicomputers (VMS), workstations (UNIX), OS/2, the Commodore Amiga and the Sinclair QL.
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Trellis may refer to:
  • Trellis (agriculture), a structure that supports climbing plants
  • Trellis (graph), a special kind of graph, often used in coding
  • Trellis modulation, also known as "trellis coded modulation", in telecommunications

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