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 A322063 Number of ways to choose a stable partition of an antichain of sets spanning n vertices. 2
 1, 1, 3, 25, 773, 160105 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A stable partition of a hypergraph or set system is a set partition of the vertices where no non-singleton edge has all its vertices in the same block. LINKS EXAMPLE The a(3) = 25 stable partitions of antichains on 3 vertices. The antichain is on top, and below is a list of all its stable partitions.   {1}{2}{3}      {1,2,3}        {1}{2,3}       {1,3}{2}       {1,2}{3}   --------       --------       --------       --------       --------   {{1,2,3}}      {{1},{2,3}}    {{1,2},{3}}    {{1},{2,3}}    {{1},{2,3}}   {{1},{2,3}}    {{1,2},{3}}    {{1,3},{2}}    {{1,2},{3}}    {{1,3},{2}}   {{1,2},{3}}    {{1,3},{2}}    {{1},{2},{3}}  {{1},{2},{3}}  {{1},{2},{3}}   {{1,3},{2}}    {{1},{2},{3}}   {{1},{2},{3}} .   {1,3}{2,3}     {1,2}{2,3}     {1,2}{1,3}     {1,2}{1,3}{2,3}   --------       --------       --------       --------   {{1,2},{3}}    {{1,3},{2}}    {{1},{2,3}}    {{1},{2},{3}}   {{1},{2},{3}}  {{1},{2},{3}}  {{1},{2},{3}} MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; 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]]]]; Table[Sum[Length[stableSets[Complement[Subsets[Range[n]], Union@@Subsets/@stn], SubsetQ]], {stn, sps[Range[n]]}], {n, 5}] CROSSREFS Cf. A000110, A000569, A006125, A006126, A229048, A240936, A277203, A321979, A322064, A322065. Sequence in context: A062411 A136516 A002021 * A306792 A012764 A219275 Adjacent sequences:  A322060 A322061 A322062 * A322064 A322065 A322066 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 25 2018 STATUS approved

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Last modified August 8 05:50 EDT 2020. Contains 336290 sequences. (Running on oeis4.)