A330282 - OEIS

%I #11 Jan 05 2020 12:02:55

%S 1,2,5,52,21521

%N Number of fully chiral set-systems on n vertices.

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

%F Binomial transform of A330229.

%e The a(0) = 1 through a(2) = 5 set-systems:

%e   {}  {}     {}

%e       {{1}}  {{1}}

%e              {{2}}

%e              {{1},{1,2}}

%e              {{2},{1,2}}

%t graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]],i},{i,Length[p]}])],{p,Permutations[Union@@m]}]];

%t Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],Length[graprms[#]]==Length[Union@@#]!&]],{n,0,3}]

%Y Costrict (or T_0) set-systems are A326940.

%Y The covering case is A330229.

%Y The unlabeled version is A330294, with covering case A330295.

%Y Achiral set-systems are A083323.

%Y BII-numbers of fully chiral set-systems are A330226.

%Y Non-isomorphic fully chiral multiset partitions are A330227.

%Y Fully chiral partitions are A330228.

%Y Fully chiral factorizations are A330235.

%Y MM-numbers of fully chiral multisets of multisets are A330236.

%Y Cf. A000612, A016031, A319637, A330098, A330231, A330232, A330234.

%K nonn,more

%O 0,2

%A _Gus Wiseman_, Dec 10 2019