A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered...

coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance...

In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self-dual condition, Modular law a ≤ b implies...

In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such...

In the mathematical discipline of order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every...

partially ordered access privileges Skew lattice, a non-commutative generalization of order-theoretic lattices Lattice multiplication, a multiplication algorithm...

lattices may be incomplete. Complete lattices appear in many applications in mathematics and computer science. Both order theory and universal algebra study...

G+. If the order on the group is a linear order, then it is said to be a linearly ordered group. If the order on the group is a lattice order, i.e. any...

Introduction to Lattices and Order is a mathematical textbook on order theory by Brian A. Davey and Hilary Priestley. It was published by the Cambridge...

this partial order. A lattice is a partially ordered set that is both a meet- and join-semilattice with respect to the same partial order. Algebraically...

notion. Ideals are of great importance for many constructions in order and lattice theory. A subset I of a partially ordered set ( P , ≤ ) {\displaystyle...

introduces a momentum cut-off at the order 1/a, where a is the lattice spacing, which regularizes the theory. As a result, lattice QCD is mathematically well-defined...

In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (1850), is an infinite array of discrete points generated by a set of...

special use of the term refers to complete partial orders or complete lattices. However, many other interesting notions of completeness exist. The motivation...

mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8. The name...

in functional analysis and order theory, a Banach lattice (X,‖·‖) is a complete normed vector space with a lattice order, ≤ {\displaystyle \leq } , such...

expansion (a(bc))d = a((bc)d), so in the ordering of the Tamari lattice (a(bc))d ≤ a((bc)d). In this partial order, any two groupings g1 and g2 have a greatest...

In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing...

infima. Most of these apply to partially ordered sets that are at least lattices, but the concept can in fact reasonably be generalized to semilattices...

meet-semilattice is a lattice. A lattice in which every subset, not just every pair, possesses a meet and a join is a complete lattice. It is also possible...

that are related to the fields of order, lattice, and domain theory. Note that there is a structured list of order topics available as well. Other helpful...

Niemeier lattice for each of these Dynkin diagrams. The complete list of Niemeier lattices is given in the following table. In the table, G0 is the order of...

Completeness (order theory) Dense order Distributivity (order theory) Modular lattice Distributive lattice Completely distributive lattice Ascending chain...

generalizations a lattice ordered group, a group that with a partial ordering that is a lattice order This disambiguation page lists mathematics articles associated...

In the mathematical areas of order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following:...

The division lattice is an infinite complete bounded distributive lattice whose elements are the natural numbers ordered by divisibility. Its least element...

subgroups of G {\displaystyle G} , with the partial ordering being set inclusion. In this lattice, the join of two subgroups is the subgroup generated...

Bethe lattice (also called a regular tree) is an infinite symmetric regular tree where all vertices have the same number of neighbors. The Bethe lattice was...

The concept of a lattice arises in order theory, a branch of mathematics. The Hasse diagram below depicts the inclusion relationships among some important...

matroids and lattices, a geometric lattice is a finite atomistic semimodular lattice, and a matroid lattice is an atomistic semimodular lattice without the...