# Discrete Mathematics & Theoretical Computer Science

## Volume 6 n° 2 (2004), pp. 163-190

author: | Caspard, Nathalie and Monjardet, Bernard |
---|---|

title: | Some lattices of closure systems on a finite set |

keywords: | Anti-exchange closure operator, closure system, convex geometry, (locally distributive) lattice, quasi-closed set. |

abstract: | In this paper we study two lattices of significant particular closure systems on a finite set, namely the union stable
closure systems and the convex geometries. Using the notion of
(admissible) quasi-closed set and of (deletable) closed set, we
determine the covering relation ≺ of these lattices
and the changes induced, for instance, on the irreducible elements
when one goes from C to C' where
C and C' are two such closure systems
satisfying C ≺ C'. We also do a systematic study of
these lattices of closure systems, characterizing for instance their
join-irreducible and their meet-irreducible elements.
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reference: | Caspard, Nathalie and Monjardet, Bernard (2004),
Some lattices of closure systems on a finite set,
Discrete Mathematics and Theoretical Computer Science 6, pp. 163-190 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Sun Jun 20 22:42:13 CEST 2004 by gustedt