Article,
The core of finite lattices
Discrete Mathematics, 88 (2-3): 133 - 147 (1991)
DOI: 10.1016/0012-365X(91)90005-M
Abstract
The meet-core of a finite lattice L is its minimal -- in fact minimum -- partial meet- subsemilattice of which the filter lattice is isomorphic to L. This gives a representation theory for finite lattices, in particular which extends Birkhoff's correspondence between ordered sets and distributive lattices, and is linked with Wille's notion of scaffolding. The meet-cores (and dually the join-cores) of modular, geometric and join-meet-distributive lattices are characterized locally by some obligatory sublattices or by some construction procedures otherwise.
