About The Recursive Decomposition of the lattice of co-Moore Families

Given a set Un = {0, 1, ..., n − 1}, a collection M of subsets of Un that is closed under intersection and contains Un is known as a Moore family. The set of Moore families for a fixed n is in bijection with the set of Moore co-families (union-closed families containing the empty set) denoted itself Mn. In this paper, we propose for the first time a recursive definition of the set of Moore co-families on Un. These results follow the work carried out in [1] to enumerate the number of Moore families on U7.