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A358944
Number of Green's L-classes in B_n, the semigroup of binary relations on [n].
0
1, 2, 7, 55, 1324, 120633, 36672159
OFFSET
0,2
COMMENTS
Each L-class in B_n is determined by a union closed family of subsets of [n] that is generated by a basis of size at most n.
REFERENCES
K. H. Kim, Boolean Matrix Theory and Applications, Marcel Decker Inc., 1982.
FORMULA
a(n) = Sum_{k=0..n} A355315(n,k).
MATHEMATICA
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 &] &, able[Table[Length[Select[Subsets[Tuples[{0, 1}, nn], {i}], independentQ[#] &]], {i, 0, nn}], {nn, 0, 5}]]]
CROSSREFS
Sequence in context: A371828 A227381 A182055 * A366456 A211209 A363205
KEYWORD
nonn,hard,more
AUTHOR
Geoffrey Critzer, Jan 16 2023
STATUS
approved