Gabriela Bordalo (Centro de Algebra da Universidade de Lisboa - Universidade de Lisboa) Nathalie Caspard (LACL - Laboratoire d'Algorithmique Complexité et Logique - CNRS : FRE2673 - Université Paris XII Val de Marne) Bernard Monjardet () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
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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.
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Length: Date of creation: 01 Aug 2008 Date of revision: Handle: RePEc:hal:cesptp:halshs-00308785_v1
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