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Going down in (semi)lattices of finite Moore families and convex geometries
Abstract : In this paper we first study the changes occuring 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 show that the poset of all convex geometries that have the same poset of join-irreducible elements is a ranked join-semilattice, and we give an algorithm for computing it. Finally, 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.
Cited literature [22 references]
https://halshs.archives-ouvertes.fr/halshs-00308785
Contributor : Bernard Monjardet <>
Submitted on : Friday, August 1, 2008 - 4:21:15 PM
Last modification on : Sunday, January 19, 2020 - 6:38:22 PM
Document(s) archivé(s) le : Thursday, June 3, 2010 - 5:35:41 PM
Contributor : Bernard Monjardet <>
Submitted on : Friday, August 1, 2008 - 4:21:15 PM
Last modification on : Sunday, January 19, 2020 - 6:38:22 PM
Document(s) archivé(s) le : Thursday, June 3, 2010 - 5:35:41 PM
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