Going down in (semi)lattices of finite Moore families and convex geometries

Title:

Going down in (semi)lattices of finite Moore families and convex geometries

Creator:

Bordalo, Gabriela, Caspard, Nathalie, and Monjardet, Bernard

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:aa3ea361-1dba-4aac-b5f9-a644ce982d8a
uuid:aa3ea361-1dba-4aac-b5f9-a644ce982d8a

Subject:

closure system, Moore family, convex geometry, (semi)lattice, and algorithm

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we first study what changes occur in the posets of irreducible elements when one goes from an arbitrary Moore family (respectively, a convex geometry) to one of its lower covers in the lattice of all Moore families (respectively, in the semilattice of all convex geometries) defined on a finite set. Then we study the set of all convex geometries which have the same poset of join-irreducible elements. We show that this set---ordered by set inclusion---is a ranked join-semilattice and we characterize its cover relation. We prove that the lattice of all ideals of a given poset $P$ is the only convex geometry having a poset of join-irreducible elements isomorphic to $P$ if and only if the width of $P$ is less than 3. Finally, we give an algorithm for computing all convex geometries having the same poset of join-irreducible elements.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

249-271

Source:

Czechoslovak Mathematical Journal | 2009 Volume:59 | Number:1

Harvested from:

CDK

Metadata only:

false