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A326362 Number of maximal intersecting antichains of nonempty, non-singleton subsets of {1..n}. 12

%I

%S 1,1,1,2,16,163,11742

%N Number of maximal intersecting antichains of nonempty, non-singleton subsets of {1..n}.

%C A set system (set of sets) is an antichain if no part is a subset of any other, and is intersecting if no two parts are disjoint.

%F For n > 1, a(n) = A326363(n) - n - 1 = A007363(n + 1) - n.

%e The a(4) = 16 maximal intersecting antichains:

%e {{1,2,3,4}}

%e {{1,2},{1,3},{2,3}}

%e {{1,2},{1,4},{2,4}}

%e {{1,3},{1,4},{3,4}}

%e {{2,3},{2,4},{3,4}}

%e {{1,2},{1,3,4},{2,3,4}}

%e {{1,3},{1,2,4},{2,3,4}}

%e {{1,4},{1,2,3},{2,3,4}}

%e {{2,3},{1,2,4},{1,3,4}}

%e {{2,4},{1,2,3},{1,3,4}}

%e {{3,4},{1,2,3},{1,2,4}}

%e {{1,2},{1,3},{1,4},{2,3,4}}

%e {{1,2},{2,3},{2,4},{1,3,4}}

%e {{1,3},{2,3},{3,4},{1,2,4}}

%e {{1,4},{2,4},{3,4},{1,2,3}}

%e {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}

%t stableSets[u_,Q_]:=If[Length[u]==0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r==w||Q[r,w]||Q[w,r]],Q]]]];

%t fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];

%t Table[Length[fasmax[stableSets[Subsets[Range[n],{2,n}],Or[Intersection[#1,#2]=={},SubsetQ[#1,#2]]&]]],{n,0,5}]

%Y Antichains of nonempty, non-singleton sets are A307249.

%Y Minimal covering antichains are A046165.

%Y Maximal intersecting antichains are A007363.

%Y Maximal antichains of nonempty sets are A326359.

%Y Cf. A000372, A003182, A006126, A006602, A014466, A051185, A058891, A261005, A305000, A305844, A326358, A326360, A326361, A326363.

%K nonn,more

%O 0,4

%A _Gus Wiseman_, Jul 01 2019

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Last modified April 5 23:20 EDT 2020. Contains 333260 sequences. (Running on oeis4.)