A299116
The number of sparse union-closed sets. That is, the number of union-closed sets on n elements containing the empty set and the universe, such that in average each set (not counting the empty set) has at most n/2 elements.
Original entry on oeis.org
0, 0, 0, 2, 27, 3133, 5777931
Offset: 1
A358944
Number of Green's L-classes in B_n, the semigroup of binary relations on [n].
Original entry on oeis.org
1, 2, 7, 55, 1324, 120633, 36672159
Offset: 0
- K. H. Kim, Boolean Matrix Theory and Applications, Marcel Decker Inc., 1982.
-
independentQ[collection_] := If[MemberQ[collection, Table[0, {nn}]] \[Or] !
DuplicateFreeQ[collection], False,Apply[And,Table[! MemberQ[ Map[Clip[Total[#]] &, Subsets[Drop[collection, {i}], {2, Length[collection]}]],
collection[[i]]], {i, 1, Length[collection]}]]]; Map[Total,
Map[Select[#, # > 0 &] &, Table[Table[Length[Select[Subsets[Tuples[{0, 1}, nn], {i}], independentQ[#] &]], {i, 0, nn}], {nn, 0, 5}]]]
A367565
Number of reduced contexts on n labeled objects.
Original entry on oeis.org
1, 3, 32, 1863, 1316515, 75868099847
Offset: 1
The a(2)=3 set systems are {{1},{2}}, {{},{1}}, and {{},{2}}. The corresponding formal contexts represented by crosstables are
1 x. 1 .x 1 ..
2 .x 2 .. 2 x. .
- B. Ganter and R. Wille, Formal Concept Analysis, Springer-Verlag, 1999, ISBN 3-540-62771-5, p. 24.
- B. Ganter and S. A. Obiedkov, Conceptual Exploration, Springer 2016, ISBN 978-3-662-49290-1, pages 1-315.
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