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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