A358944 Number of Green's L-classes in B_n, the semigroup of binary relations on [n].
1, 2, 7, 55, 1324, 120633, 36672159
Offset: 0
References
- K. H. Kim, Boolean Matrix Theory and Applications, Marcel Decker Inc., 1982.
Programs
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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 &] &, Table[Table[Length[Select[Subsets[Tuples[{0, 1}, nn], {i}], independentQ[#] &]], {i, 0, nn}], {nn, 0, 5}]]]
Formula
a(n) = Sum_{k=0..n} A355315(n,k).
Comments