

A326946


Number of unlabeled T_0 setsystems on n vertices.


17




OFFSET

0,2


COMMENTS

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks 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..4.


FORMULA

Partial sums of A319637.
a(n) = A326949(n)/2.


EXAMPLE

Nonisomorphic representatives of the a(0) = 1 through a(2) = 5 setsystems:
{} {} {}
{{1}} {{1}}
{{1},{2}}
{{2},{1,2}}
{{1},{2},{1,2}}


MATHEMATICA

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


CROSSREFS

The nonT_0 version is A000612.
The antichain case is A245567.
The covering case is A319637.
The labeled version is A326940.
The version with empty edges allowed is A326949.
Cf. A003180, A055621, A059052, A059201, A316978, A319559, A319564, A326942.
Sequence in context: A277436 A002665 A192222 * A241586 A000665 A058882
Adjacent sequences: A326943 A326944 A326945 * A326947 A326948 A326949


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Aug 08 2019


STATUS

approved



