Generation of Union-Closed Sets and Moore Families
Gunnar Brinkmann and Robin Deklerck
Applied Mathematics, Computer Science and Statistics
Krijgslaan 281 S9
We describe an algorithm to constructively enumerate
non-isomorphic union-closed sets and Moore sets. We confirm the number
of isomorphism classes of union-closed sets and Moore sets on n
elements presented by other authors, and give the number of isomorphism
classes of union-closed sets and Moore sets on 7 elements. Due to the
enormous growth of the number of isomorphism classes, it seems unlikely
that constructive enumeration for 8 or more elements will be possible
in the foreseeable future.
Full version: pdf,
(Concerned with sequences
Received November 20 2017; revised version received February 5 2018.
Published in Journal of Integer Sequences, February 8 2018.
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