The number of Moore families on n=6

This paper studies the generating problem for Moore families on an n-set (i.e. families closed under intersection containing the n-set) or closure operators. We show a bijection between Moore families and ideal color sets of the colored poset based on n.2n-1, where n.2n-1 is the sum of n Boolean lattices with n-1 atoms. By applying an algorithm to generate ideal color sets, we can determine that the number of Moore families on 6 elements is exactly 75 973 751 474.