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 A327356 Number of connected separable antichains of nonempty sets covering n vertices (vertex-connectivity 1). 4
 0, 0, 1, 3, 40, 1365 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS An antichain is a set of sets, none of which is a subset of any other. It is covering if there are no isolated vertices. The vertex-connectivity of a set-system is the minimum number of vertices that must be removed (along with any resulting empty edges) to obtain a non-connected set-system or singleton. Note that this means a single node has vertex-connectivity 0. LINKS EXAMPLE Non-isomorphic representatives of the a(4) = 40 set-systems:   {{1,2},{1,3,4}}   {{1,2},{1,3},{1,4}}   {{1,2},{1,3},{2,4}}   {{1,2},{1,3},{1,4},{2,3}} MATHEMATICA csm[s_]:=With[{c=Select[Subsets[Range[Length[s]], {2}], Length[Intersection@@s[[#]]]>0&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]]; 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]]]]; vertConnSys[vts_, eds_]:=Min@@Length/@Select[Subsets[vts], Function[del, Length[del]==Length[vts]-1||csm[DeleteCases[DeleteCases[eds, Alternatives@@del, {2}], {}]]!={Complement[vts, del]}]]; Table[Length[Select[stableSets[Subsets[Range[n], {1, n}], SubsetQ], vertConnSys[Range[n], #]==1&]], {n, 0, 4}] CROSSREFS Column k = 1 of A327351. The graphical case is A327336. The unlabeled version is A327436. Cf. A014466, A048143, A307249, A326786, A326950, A327062, A327112, A327114, A327334. Sequence in context: A012250 A094330 A110468 * A295612 A286661 A171058 Adjacent sequences:  A327353 A327354 A327355 * A327357 A327358 A327359 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 11 2019 STATUS approved

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Last modified September 29 07:28 EDT 2020. Contains 337425 sequences. (Running on oeis4.)