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• In one mathematical usage, a lattice is a partially ordered set (poset) in which any two elements have a supremum and an infimum. The Hasse diagrams of these posets look (in some simple cases) like the aforementioned lattices. See lattice (order) for a detailed treatment.

• In another mathematical usage, a lattice is a discrete subgroup of Rⁿ that spans Rⁿ as a real vector space. The elements of a lattice are regularly spaced, reminiscent of the intersection points of a lath lattice. See lattice (group), lattice point problems .
  • This concept is used in materials science, in which a lattice is a 3-dimensional array of regularly spaced points coinciding with the atom or molecule positions in a crystal.
  • It also occurs in computational physics, in which a lattice is an n-dimensional geometrical structure of sites, connected by bonds, which represent positions which may be occupied by atoms, molecules, electrons, spins, etc. For an article dealing with the formal representation of such structures see Lattice Geometries. Different types of lattice modelIn physics, a lattice model is a physical model that is not defined on a continuum, but on a lattice, which is a graph or an n complex approximating spacetime or space. The lattice is translationally invariant if it is generated by a subgroup of translatis are used in physics, mathematics, and finance.

• In digital signal processingDigital signal processing DSP is the study of signals in a digital representation and the processing methods of these signals. DSP and analog signal processing are subsets of signal processing. It has three major subfields: audio signal processing, digita, lattice filter s are electronic filterAn electronic filter eliminates unwanted frequencies from an electronic signal. There are several kinds of electronic filters: A low-pass filter passes low frequencies. A high-pass filter passes high frequencies. A band-pass filter passes a limited ranges with a special recursive structure.

• In musicMusic often an art/ entertainment, is a total social fact whose definitions vary according to era and culture," according to Jean Molino. 1 It is often contrasted with noise. According to musicologist Jean-Jacques Nattiez: "The border between music and no lattices are often used to model pitch spaceIn music pitch space is pitch relations, ie nearness or farness, represented through geometric models, most often multi dimensional, how near or far pitches are from each other. Cognitive psychologists including Longuet-Higgins (1978) and Shepard (1982),, especially just intonationJust intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. Any interval tuned in this way is called a just interval . Another way of considering just intonation is as being based on members of the harmonic. See: TonalSoft.com: Lattices Text and diagrams © 1998 by Joseph L. Monzo.

• Lattice CorporationLattice C (according to its author, Lattice Corporation) was the first C compiler for 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 Sinc made some of the first compilerA compiler is a computer program that translates a computer program written in one computer language (called the source language into an equivalent program written in another computer language (called the output or the target language . Introduction and hs for PCs.

• Lattice Semiconductor [1] is a company which makes FPGAs and related electronics products.

• In baking, various pastries and pies can be made with a lattice pattern, and special cutters are available to facilitate the creation of such patterns.