

A307249


Number of simplicial complexes with n nodes.


32




OFFSET

0,3


COMMENTS

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 noncovering case is A014466.


LINKS

Table of n, a(n) for n=0..8.
Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.


FORMULA

Inverse binomial transform of A014466.


EXAMPLE

Maximal simplices of the a(0) = 1 through a(3) = 9 simplicial complexes:
{} {{1}} {{12}} {{123}}
{{1}{2}} {{1}{23}}
{{2}{13}}
{{3}{12}}
{{12}{13}}
{{12}{23}}
{{13}{23}}
{{1}{2}{3}}
{{12}{13}{23}}


MATHEMATICA

nn=5;
stableSets[u_, Q_]:=If[Length[u]===0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r===wQ[r, w]Q[w, r]], Q]]]];
Table[Length[stableSets[Subsets[Range[n], {2, n}], SubsetQ]], {n, 0, nn}]


CROSSREFS

Cf. A000372, A003182, A006126, A006602, A014466, A261005, A293606, A293993, A305000, A305844, A306550, A317674, A319721, A320449.
Sequence in context: A337043 A008269 A039718 * A201381 A075538 A067965
Adjacent sequences: A307246 A307247 A307248 * A307250 A307251 A307252


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Mar 31 2019


STATUS

approved



