

A326959


Number of T_0 setsystems covering a subset of {1..n} that are closed under intersection.


5




OFFSET

0,2


COMMENTS

A setsystem is a finite set of finite nonempty sets. 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}}. The T_0 condition means that the dual is strict (no repeated edges).


LINKS

Table of n, a(n) for n=0..8.


FORMULA

Binomial transform of A309615.


EXAMPLE

The a(0) = 1 through a(3) = 22 setsystems:
{} {} {} {}
{{1}} {{1}} {{1}}
{{2}} {{2}}
{{1},{1,2}} {{3}}
{{2},{1,2}} {{1},{1,2}}
{{1},{1,3}}
{{2},{1,2}}
{{2},{2,3}}
{{3},{1,3}}
{{3},{2,3}}
{{1},{1,2},{1,3}}
{{2},{1,2},{2,3}}
{{3},{1,3},{2,3}}
{{1},{1,2},{1,2,3}}
{{1},{1,3},{1,2,3}}
{{2},{1,2},{1,2,3}}
{{2},{2,3},{1,2,3}}
{{3},{1,3},{1,2,3}}
{{3},{2,3},{1,2,3}}
{{1},{1,2},{1,3},{1,2,3}}
{{2},{1,2},{2,3},{1,2,3}}
{{3},{1,3},{2,3},{1,2,3}}


MATHEMATICA

dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}];
Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], UnsameQ@@dual[#]&&SubsetQ[#, Intersection@@@Tuples[#, 2]]&]], {n, 0, 3}]


CROSSREFS

The covering case is A309615.
T_0 setsystems are A326940.
The version with empty edges allowed is A326945.
Cf. A051185, A058891, A059201, A316978, A319559, A309615, A319637, A326943, A326944, A326946, A326947, A326959.
Sequence in context: A068413 A137069 A050994 * A034384 A078419 A241428
Adjacent sequences: A326956 A326957 A326958 * A326960 A326961 A326962


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Aug 13 2019


EXTENSIONS

a(5)a(8) from Andrew Howroyd, Aug 14 2019


STATUS

approved



