cp's OEIS Frontend

A330229 Number of fully chiral set-systems covering n vertices.

%I A330229 #9 Dec 13 2019 19:46:37
%S A330229 1,1,2,42,21336
%N A330229 Number of fully chiral set-systems covering n vertices.
%C A330229 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.
%F A330229 Binomial transform is A330282.
%e A330229 The a(3) = 42 set-systems:
%e A330229   {1}{2}{13}    {1}{2}{12}{13}    {1}{2}{12}{13}{123}
%e A330229   {1}{2}{23}    {1}{2}{12}{23}    {1}{2}{12}{23}{123}
%e A330229   {1}{3}{12}    {1}{3}{12}{13}    {1}{3}{12}{13}{123}
%e A330229   {1}{3}{23}    {1}{3}{13}{23}    {1}{3}{13}{23}{123}
%e A330229   {2}{3}{12}    {2}{3}{12}{23}    {2}{3}{12}{23}{123}
%e A330229   {2}{3}{13}    {2}{3}{13}{23}    {2}{3}{13}{23}{123}
%e A330229   {1}{12}{23}   {1}{2}{13}{123}
%e A330229   {1}{13}{23}   {1}{2}{23}{123}
%e A330229   {2}{12}{13}   {1}{3}{12}{123}
%e A330229   {2}{13}{23}   {1}{3}{23}{123}
%e A330229   {3}{12}{13}   {2}{3}{12}{123}
%e A330229   {3}{12}{23}   {2}{3}{13}{123}
%e A330229   {1}{12}{123}  {1}{12}{23}{123}
%e A330229   {1}{13}{123}  {1}{13}{23}{123}
%e A330229   {2}{12}{123}  {2}{12}{13}{123}
%e A330229   {2}{23}{123}  {2}{13}{23}{123}
%e A330229   {3}{13}{123}  {3}{12}{13}{123}
%e A330229   {3}{23}{123}  {3}{12}{23}{123}
%t A330229 graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]],i},{i,Length[p]}])],{p,Permutations[Union@@m]}]];
%t A330229 Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],Union@@#==Range[n]&&Length[graprms[#]]==n!&]],{n,0,3}]
%Y A330229 The non-covering version is A330282.
%Y A330229 Costrict (or T_0) covering set-systems are A059201.
%Y A330229 BII-numbers of fully chiral set-systems are A330226.
%Y A330229 Non-isomorphic, fully chiral multiset partitions are A330227.
%Y A330229 Fully chiral partitions are counted by A330228.
%Y A330229 Fully chiral covering set-systems are A330229.
%Y A330229 Fully chiral factorizations are A330235.
%Y A330229 MM-numbers of fully chiral multisets of multisets are A330236.
%Y A330229 Cf. A000612, A055621, A083323, A283877, A319559, A319564, A330224, A330234.
%K A330229 nonn,more
%O A330229 0,3
%A A330229 _Gus Wiseman_, Dec 08 2019