

A327052


Number of T_0 (costrict) setsystems covering a subset of {1..n} where every two covered vertices appear together in some edge (cointersecting).


8




OFFSET

0,2


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 setsystems whose dual is strict and pairwise intersecting.


LINKS

Table of n, a(n) for n=0..4.


FORMULA

Binomial transform of A327053.


EXAMPLE

The a(0) = 1 through a(2) = 6 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}]], UnsameQ@@dual[#]&&stableQ[dual[#], Intersection[#1, #2]=={}&]&]], {n, 0, 3}]


CROSSREFS

The unlabeled multiset partition version is A319760.
The nonT_0 version is A327039.
The covering case is A327053.
Cf. A051185, A319752, A319774, A327038, A327040.
Sequence in context: A065410 A000721 A262279 * A231508 A136306 A274825
Adjacent sequences: A327049 A327050 A327051 * A327053 A327054 A327055


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Aug 18 2019


STATUS

approved



