Some lattices of closure systems on a finite set - Archive ouverte HAL Access content directly
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2004

Some lattices of closure systems on a finite set

(1) , (2)
1
2

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 \prec 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 \prec C'. We also do a systematic study of these lattices of closure systems, characterizing for instance their join-irreducible and their meet-irreducible elements.
Fichier principal
Vignette du fichier
dm060202.pdf (223.65 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00959003 , version 1 (13-03-2014)

Identifiers

Cite

Nathalie Caspard, Bernard Monjardet. Some lattices of closure systems on a finite set. Discrete Mathematics and Theoretical Computer Science, 2004, Vol. 6 no. 2 (2), pp.163-190. ⟨10.46298/dmtcs.309⟩. ⟨hal-00959003⟩
131 View
699 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More