|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.
If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files.
|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.|
|ps.gz-source:||dm060202.ps.gz (92 K)|
|ps-source:||dm060202.ps (267 K)|
|pdf-source:||dm060202.pdf (244 K)|
The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.
Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.