

A327040


Number of setsystems covering n vertices, every two of which appear together in some edge (cointersecting).


16




OFFSET

0,3


COMMENTS

A setsystem is a finite set of finite nonempty sets. Its elements are sometimes called edges. The dual of a setsystem 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 setsystems that are cointersecting, meaning their dual is pairwise intersecting.


LINKS



FORMULA

Inverse binomial transform of A327039.


EXAMPLE

The a(0) = 1 through a(2) = 4 setsystems:
{} {{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

The unlabeled multiset partition version is A319752.
The BIInumbers of these setsystems are A326853.
The pairwise intersecting case is A327037.
The noncovering version is A327039.
The case where the dual is strict is A327053.


KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



