OFFSET
0,3
COMMENTS
A set-system is a finite set of finite nonempty sets. Its elements are sometimes called edges. The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. This sequence counts covering set-systems that are cointersecting, meaning their dual is pairwise intersecting.
FORMULA
Inverse binomial transform of A327039.
EXAMPLE
The a(0) = 1 through a(2) = 4 set-systems:
{} {{1}} {{1,2}}
{{1},{1,2}}
{{2},{1,2}}
{{1},{2},{1,2}}
MATHEMATICA
dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], Union@@#==Range[n]&&stableQ[dual[#], Intersection[#1, #2]=={}&]&]], {n, 0, 3}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 18 2019
EXTENSIONS
a(5)-a(7) from Christian Sievers, Oct 22 2023
STATUS
approved