%0 Journal Article %1 Duquenne1991133 %A Duquenne, Vincent %D 1991 %J Discrete Mathematics %K concept core fca lattice structure %N 2-3 %P 133 - 147 %R 10.1016/0012-365X(91)90005-M %T The core of finite lattices %U http://www.sciencedirect.com/science/article/B6V00-45GMF6D-5/2/1120caa94c245d57b16992536b46325d %V 88 %X 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.

@article{Duquenne1991133, 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.}, added-at = {2018-12-15T14:39:54.000+0100}, author = {Duquenne, Vincent}, biburl = {https://www.bibsonomy.org/bibtex/23754f36ef7da2a619c34a7c863ba3427/tomhanika}, description = {ScienceDirect - Discrete Mathematics : The core of finite lattices}, doi = {10.1016/0012-365X(91)90005-M}, interhash = {3fcc87180a838828f74fd82d7b6ac209}, intrahash = {3754f36ef7da2a619c34a7c863ba3427}, issn = {0012-365X}, journal = {Discrete Mathematics}, keywords = {concept core fca lattice structure}, number = {2-3}, pages = {133 - 147}, timestamp = {2018-12-15T14:39:54.000+0100}, title = {The core of finite lattices}, url = {http://www.sciencedirect.com/science/article/B6V00-45GMF6D-5/2/1120caa94c245d57b16992536b46325d}, volume = 88, year = 1991 }