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distributive lattice

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(algebra) A lattice in which the "meet" and the "join" operations are distributive with respect to each other.

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Monteiro in [9[ for the free distributive lattice over a poset.
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Young's lattice given by the inclusion ordering of Young diagrams representing integer partitions is a distributive lattice.
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Distributive lattices are ubiquitous but also rather specific structures.
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This distributivity law defines the class of distributive lattices.
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Such structures are called completely distributive lattices.
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Every distributive lattice is modular.
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The number of elements in free distributive lattices with n generators is given by the Dedekind numbers.
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Completely distributive complete lattices (also called completely distributive lattices for short) are indeed highly special structures.
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The simplest non-distributive lattices are M3, the "diamond lattice", and N5, the "pentagon lattice".
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A further important representation was established by Hilary Priestley in her representation theorem for distributive lattices.
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This condition is called distributivity and gives rise to distributive lattices.
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It characterizes distributive lattices as the lattices of compact open sets of certain topological spaces.
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See the article on completely distributive lattices.
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The covering relation of any finite distributive lattice forms a median graph.
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This definition of distributivity allows generalizing some statements about distributive lattices to distributive semilattices.
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The free distributive lattice over a set of generators G can be constructed much more easily than a general free lattice.
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This establishes a bijection (up to isomorphism) between the class of all finite posets and the class of all finite distributive lattices.
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(b) Verify that the non-distributive lattice in Fig. 14-7(b) is modular; hence the converse of (a) is not true.
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This bijection can be extended to a duality of categories between homomorphisms of finite distributive lattices and monotone functions of finite posets.
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As a consequence of Stone's and Priestley's theorems, one easily sees that any distributive lattice is really isomorphic to a lattice of sets.
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Another early representation theorem is now known as Stone's representation theorem for distributive lattices (the name honors Marshall Harvey Stone, who first proved it).
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The natural numbers form a (conditionally complete) distributive lattice by taking the greatest common divisor as meet and the least common multiple as join.
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A variant, Stone's representation theorem for lattices states that every distributive lattice is isomorphic to a sublattice of the power set lattice of some set.
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As in the case of arbitrary lattices, one can choose to consider a distributive lattice L either as a structure of order theory or of universal algebra.
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More generally, every median graph gives rise to a ternary operation m satisfying idempotence, commutativity, and distributivity, but possibly without the identity elements of a distributive lattice.
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