Lattice (mathematics)

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In mathematics, the term lattice can mean:

• A partially ordered set (poset) in which any two elements have a supremum and an infimum—see lattice (order). The Hasse diagrams of these posets look (in some simple cases) like the lattices of ordinary language. These lattices can also be defined as algebraic structures.

• A discrete subgroup of Rⁿ that spans it as a real vector space, or its translate—see lattice (group). The elements of a lattice are regularly spaced, reminiscent of the intersection points of a lath lattice. Special types include unimodular lattices, the Leech lattice, and the Niemeier lattice. See also translational symmetry.

• A lattice graph is a planar graph whose drawing can correspond to a lattice.

• More generally, a lattice in a locally compact topological group is a discrete subgroup of finite covolume—see lattice (discrete subgroup).

• The lattice method or form (also known as the jalousie method) is an algorithm used to teach basic multiplication to elementary grades.

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