On the number of databases and closure operations
Theoretical Computer Science
Functional dependencies in relational databases: a lattice point of view
Discrete Applied Mathematics - Special issue on combinatorial problems in databases
Latticial structures in data analysis
Theoretical Computer Science
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Knowledge Spaces
Functional Dependencies and the Semilattice of Closed Classes
MFDBS '89 Proceedings of the 2nd Symposium on Mathematical Fundamentals of Database Systems
Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
Counting of moore families for n=7
ICFCA'10 Proceedings of the 8th international conference on Formal Concept Analysis
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A collection of sets on a ground set U n (U n 驴=驴{1,2,...,n}) closed under intersection and containing U n 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 $\mathbb{M}_n$ . In this paper, we propose a recursive definition of the set of Moore co-families on U n . Then we apply this decomposition result to compute a lower bound on $|\mathbb M_n|$ as a function of $|\mathbb M_{n-1}|$ , the Dedekind numbers and the binomial coefficients. These results follow the work carried out in [1] to enumerate the number of Moore families on U 7.