A collection of sets on a ground set Un (Un denotes the set f1; 2; :::; ng) closed under intersection and containing Un is known as a Moore family. The set of Moore families for a xed n is in bijection with the set of Moore co-families (union-closed families containing the empty set) denoted Mn. In this paper, we show that the set Mn can be endowed with the quotient partition associated with some operator h. This operator h is the main concept underlying a recursive description of Mn. By this way each class of the partition contains all the families which have the same image by h. Then we prove some structural results linking any Moore co-family to its image by h. From these results we derive an algorithm which computes eciently the image by h of any given Moore co-family.
L. Beaudou et al.