Look up lattice in Wiktionary, the free dictionary. This disambiguation page lists articles associated with the title Lattice. If an internal link led you here, you may wish to change lattice in discrete mathematics pdf link to point directly to the intended article.

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This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. A lattice in the Euclidean plane. A lattice may be viewed as a regular tiling of a space by a primitive cell.

Lattices have many significant applications in pure mathematics, particularly in connection to Lie algebras, number theory and group theory. They also arise in applied mathematics in connection with coding theory, in cryptography because of conjectured computational hardness of several lattice problems, and are used in various ways in the physical sciences. For instance, in materials science and solid-state physics, a lattice is a synonym for the “frame work” of a crystalline structure, a 3-dimensional array of regularly spaced points coinciding in special cases with the atom or molecule positions in a crystal.

More generally, lattice models are studied in physics, often by the techniques of computational physics. A lattice is the symmetry group of discrete translational symmetry in n directions.