

A326940


Number of T_0 setsystems on n vertices.


16



1, 2, 7, 112, 32105, 2147161102, 9223372004645756887, 170141183460469231537996491362807709908, 57896044618658097711785492504343953921871039195927143534469727707459805807105
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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, counted with multiplicity. 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



FORMULA



EXAMPLE

The a(0) = 1 through a(2) = 7 setsystems:
{} {} {}
{{1}} {{1}}
{{2}}
{{1},{2}}
{{1},{1,2}}
{{2},{1,2}}
{{1},{2},{1,2}}


MATHEMATICA

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


CROSSREFS

The nonT_0 version is A058891 shifted to the left.
The version with empty edges is A326941.


KEYWORD

nonn


AUTHOR



STATUS

approved



