

A330282


Number of fully chiral setsystems on n vertices.


6




OFFSET

0,2


COMMENTS

A setsystem is a finite set of finite nonempty sets. It is fully chiral if every permutation of the covered vertices gives a different representative.


LINKS



FORMULA



EXAMPLE

The a(0) = 1 through a(2) = 5 setsystems:
{} {} {}
{{1}} {{1}}
{{2}}
{{1},{1,2}}
{{2},{1,2}}


MATHEMATICA

graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]], i}, {i, Length[p]}])], {p, Permutations[Union@@m]}]];
Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], Length[graprms[#]]==Length[Union@@#]!&]], {n, 0, 3}]


CROSSREFS

Costrict (or T_0) setsystems are A326940.
BIInumbers of fully chiral setsystems are A330226.
Nonisomorphic fully chiral multiset partitions are A330227.
Fully chiral partitions are A330228.
Fully chiral factorizations are A330235.
MMnumbers of fully chiral multisets of multisets are A330236.


KEYWORD

nonn,more


AUTHOR



STATUS

approved



