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A330229
Number of fully chiral set-systems covering n vertices.
14
1, 1, 2, 42, 21336
OFFSET
0,3
COMMENTS
A set-system is a finite set of finite nonempty sets. It is fully chiral if every permutation of the vertices gives a different representative.
FORMULA
Binomial transform is A330282.
EXAMPLE
The a(3) = 42 set-systems:
{1}{2}{13} {1}{2}{12}{13} {1}{2}{12}{13}{123}
{1}{2}{23} {1}{2}{12}{23} {1}{2}{12}{23}{123}
{1}{3}{12} {1}{3}{12}{13} {1}{3}{12}{13}{123}
{1}{3}{23} {1}{3}{13}{23} {1}{3}{13}{23}{123}
{2}{3}{12} {2}{3}{12}{23} {2}{3}{12}{23}{123}
{2}{3}{13} {2}{3}{13}{23} {2}{3}{13}{23}{123}
{1}{12}{23} {1}{2}{13}{123}
{1}{13}{23} {1}{2}{23}{123}
{2}{12}{13} {1}{3}{12}{123}
{2}{13}{23} {1}{3}{23}{123}
{3}{12}{13} {2}{3}{12}{123}
{3}{12}{23} {2}{3}{13}{123}
{1}{12}{123} {1}{12}{23}{123}
{1}{13}{123} {1}{13}{23}{123}
{2}{12}{123} {2}{12}{13}{123}
{2}{23}{123} {2}{13}{23}{123}
{3}{13}{123} {3}{12}{13}{123}
{3}{23}{123} {3}{12}{23}{123}
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}]], Union@@#==Range[n]&&Length[graprms[#]]==n!&]], {n, 0, 3}]
CROSSREFS
The non-covering version is A330282.
Costrict (or T_0) covering set-systems are A059201.
BII-numbers of fully chiral set-systems are A330226.
Non-isomorphic, fully chiral multiset partitions are A330227.
Fully chiral partitions are counted by A330228.
Fully chiral covering set-systems are A330229.
Fully chiral factorizations are A330235.
MM-numbers of fully chiral multisets of multisets are A330236.
Sequence in context: A193272 A193273 A182192 * A039622 A130506 A273399
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Dec 08 2019
STATUS
approved