OFFSET
0,4
COMMENTS
A set system (set of sets) is intersecting if no two edges are disjoint.
FORMULA
EXAMPLE
The a(3) = 3 intersecting set systems with empty intersection:
{}
{{1,2},{1,3},{2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}
MATHEMATICA
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[Length[Select[stableSets[Subsets[Range[n], {1, n}], Intersection[#1, #2]=={}&], And[#=={}||Intersection@@#=={}]&]], {n, 0, 4}]
CROSSREFS
The inverse binomial transform is the covering case A326364.
Set systems with empty intersection are A318129.
Intersecting set systems are A051185.
Intersecting antichains with empty intersection are A326366.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 01 2019
EXTENSIONS
a(6)-a(9) from Andrew Howroyd, Aug 12 2019
STATUS
approved