A326364 Number of intersecting set systems with empty intersection (meaning there is no vertex in common to all the edges) covering n vertices.

1, 0, 0, 2, 426, 987404, 887044205940, 291072121051815578010398, 14704019422368226413234332571239460300433492086, 12553242487939461785560846872353486129110194397301168776798213375239447299205732561174066488

Offset: 0

Author

Gus Wiseman, Jul 01 2019

Keywords

• nonn

Comments

Covering means there are no isolated vertices. A set system (set of sets) is intersecting if no two edges are disjoint.

Examples

			The a(3) = 2 intersecting set systems with empty intersection:
  {{1,2},{1,3},{2,3}}
  {{1,2},{1,3},{2,3},{1,2,3}}
		

Crossrefs

Covering set systems with empty intersection are A318128.

Covering, intersecting set systems are A305843.

Covering, intersecting antichains with empty intersection are A326365.

Cf. A006126, A007363, A014466, A051185, A058891, A305844, A307249, A318129, A326361, A326362, A326363.

Programs

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[Union@@#==Range[n],#=={}||Intersection@@#=={}]&]],{n,0,4}]

Formula

Inverse binomial transform of A326373. - Andrew Howroyd, Aug 12 2019

Extensions

a(6)-a(9) from Andrew Howroyd, Aug 12 2019