## lattice- (MATH) A periodic arrangement
of points such as the vertices of a tiling of space by cubes or the positions of atoms in a crystal. More technically,
a discrete Abelian subgroup of an
*n*-dimensional vector space which not contained in an (*n*-1)-dimensional vector space. Lattices play a central role in the theory of Lie groups, in number theory, in error-correcting codes, and many other areas of mathematics. A lattice is often, but not always, distinguished from a graph in that a lattice is a graph with a regular structure.
A**lattice path**is a sequence of points in a lattice such that each point differs from its predecessor by a finite list of allowed steps. Random lattice paths are an interesting model for the random motion of a particle and lattice paths are also important in enumerative combinatorics.
A**lattice point**is a point with integer coordinates.
- (CHEMISTRY) A regular network of fixed points about which molecules, atoms, or ions vibrate in a crystal.
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