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Keywords:
distributive lattice; congruence-uniform lattice; canonical join complex; core label order; intersection property
distributive lattice; congruence-uniform lattice; canonical join complex; core label order; intersection property
Summary:
Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices. Congruence-uniform lattices allow for a remarkable second order of their elements: the core label order; semidistributive lattices naturally possess an associated flag simplicial complex: the canonical join complex. In this article we present a characterization of finite distributive lattices in terms of the core label order and the canonical join complex, and we show that the core label order of a finite distributive lattice is always a meet-semilattice.
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