Distributive lattices and hypergraph coloring
Jim Lawrence · 1997
The "composition ideal" is a basic notion connected with free lattices.In this paper the composition ideals of distributive lattices are characterized^and the use- fulness of this characterization with respect to computation of chromatic number of hypergraphs is noted.A lattice is a triple (L,A,V), where T is a set, A and V are binary operations which are each idempotent, commutative, associative, and jointly satisfy the absorption properties:For a,b G T,aA(aV6) = a = aV(aA6).The operation A is called meet, and V is called join.We will usually denote the latticeIf T is a lattice then the set L is partially ordered by the relation:With this relation, each pair of elements have a greatest lower bound, their meet, and a least upper bound, their join.'.j