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A307249 Number of simplicial complexes with n nodes. 32


%S 1,1,2,9,114,6894,7785062,2414627396434,56130437209370320359966

%N Number of simplicial complexes with n nodes.

%C Except for a(0) = 1, this is also the number of antichains of nonempty sets covering n vertices (A006126). There are two antichains of size zero, namely {} and {{}}, while there is only one simplicial complex, namely {}. The unlabeled case is A261005. The non-covering case is A014466.

%H Gus Wiseman, <a href="/A048143/a048143_4.txt">Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons</a>.

%F Inverse binomial transform of A014466.

%e Maximal simplices of the a(0) = 1 through a(3) = 9 simplicial complexes:

%e {} {{1}} {{12}} {{123}}

%e {{1}{2}} {{1}{23}}

%e {{2}{13}}

%e {{3}{12}}

%e {{12}{13}}

%e {{12}{23}}

%e {{13}{23}}

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

%e {{12}{13}{23}}

%t nn=5;

%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 Table[Length[stableSets[Subsets[Range[n],{2,n}],SubsetQ]],{n,0,nn}]

%Y Cf. A000372, A003182, A006126, A006602, A014466, A261005, A293606, A293993, A305000, A305844, A306550, A317674, A319721, A320449.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Mar 31 2019

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Last modified April 4 21:15 EDT 2020. Contains 333229 sequences. (Running on oeis4.)