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

called an orthomodular lattice. In bounded distributive lattices, complements are unique. Every complemented distributive lattice has a unique orthocomplementation...

In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality x ⋅ ( y + z...

concept of distributivity, applied to the formation of suprema and infima. Most of these apply to partially ordered sets that are at least lattices, but the...

completely distributive lattice is a complete lattice in which arbitrary joins distribute over arbitrary meets. Formally, a complete lattice L is said...

as frames and completely distributive lattices, see distributivity in order theory. For some applications the distributivity condition is too strong,...

distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations...

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties...

are distributive lattices. Every Boolean algebra is a Heyting algebra when a → b is defined as ¬a ∨ b, as is every complete distributive lattice satisfying...

inclusion, the antichains are called Sperner families and their lattice is a free distributive lattice, with a Dedekind number of elements. More generally, counting...

duality theory for distributive lattices provides three different (but closely related) representations of bounded distributive lattices via Priestley spaces...

semilattice necessarily be bounded.) A totally ordered set is a distributive lattice, hence in particular a meet-semilattice and join-semilattice: any...

case of greedoids and of semimodular lattices, and as a generalization of partial orders and of distributive lattices. Antimatroids are equivalent, by complementation...

lattice: a lattice in which arbitrary meet and joins exist. Bounded lattice: a lattice with a greatest element and least element. Distributive lattice: a lattice...

mathematics, economics, and computer science, the lattice of stable matchings is a distributive lattice whose elements are stable matchings. For a given...

is no proper filter that is a strict superset. When a poset is a distributive lattice, maximal ideals and filters are necessarily prime, while the converse...

inverse. At the same time, semirings are a generalization of bounded distributive lattices. The smallest semiring that is not a ring is the two-element Boolean...

structure A = (A, ∨, ∧, 0, 1, ¬) such that: (A, ∨, ∧, 0, 1) is a bounded distributive lattice, and ¬ is a De Morgan involution: ¬(x ∧ y) = ¬x ∨ ¬y and ¬¬x = x...

lattices of subgroups are distributive. More generally, a finitely generated group is cyclic if and only if its lattice of subgroups is distributive and...

{\displaystyle n} -element set, the number of elements in a free distributive lattice with n {\displaystyle n} generators, and one more than the number...

DLat01 of bounded distributive lattices. Hence, DLat01 is dual to CohSp—one obtains Stone's representation theorem for distributive lattices. When restricting...

composed leads to rich algebraic structures: a preorder on graphs, a distributive lattice, and a category (one for undirected graphs and one for directed graphs)...

of N5 as a sublattice. Every distributive lattice is modular. Dilworth (1954) proved that, in every finite modular lattice, the number of join-irreducible...

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

axiomatization of Boolean algebra, such as the axioms for a complemented distributive lattice, a sufficient condition for an algebraic structure of this kind to...

Hamming distance, independent sets of vertices in path graphs, or via distributive lattices. Like the hypercube graph, the vertices of the Fibonacci cube of...

poset may be defined as a small posetal category, a distributive lattice as a small posetal distributive category, a Heyting algebra as a small posetal finitely...

graphs arise naturally in the study of ordered sets and discrete distributive lattices, and have an extensive literature". In phylogenetics, the Buneman...

sub-poset of the subsumption lattice, and is itself a lattice. This lattice, too, includes N5 and the minimal non-distributive lattice M3 as sublattices (see...

lcm(0, 0) = 0 because then the natural numbers become a complete distributive lattice with GCD as meet and LCM as join operation. This extension of the...