|
| |
|
|
A327052
|
|
Number of T_0 (costrict) set-systems covering a subset of {1..n} where every two covered vertices appear together in some edge (cointersecting).
|
|
8
|
| |
|
|
|
OFFSET
|
0,2
|
|
|
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 set-systems 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 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}]], UnsameQ@@dual[#]&&stableQ[dual[#], Intersection[#1, #2]=={}&]&]], {n, 0, 3}]
|
|
|
CROSSREFS
|
The unlabeled multiset partition version is A319760.
The non-T_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
|
| |
|
|
