HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

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.
Complete list of metadata

Cited literature [22 references]  Display  Hide  Download

Contributor : Bernard Monjardet Connect in order to contact the contributor
Submitted on : Friday, August 1, 2008 - 4:21:15 PM
Last modification on : Friday, April 29, 2022 - 10:12:36 AM
Long-term archiving on: : Thursday, June 3, 2010 - 5:35:41 PM


Files produced by the author(s)


  • HAL Id : halshs-00308785, version 1



Gabriela Bordalo, Nathalie Caspard, Bernard Monjardet. Going down in (semi)lattices of finite Moore families and convex geometries. Czechoslovak Mathematical Journal, Akademie věd České republiky, Matematický ústav, 2009, 59 (1), pp.249-271. ⟨halshs-00308785⟩



Record views


Files downloads