cp's OEIS Frontend

A330282 Number of fully chiral set-systems on n vertices.

%I A330282 #11 Jan 05 2020 12:02:55
%S A330282 1,2,5,52,21521
%N A330282 Number of fully chiral set-systems on n vertices.
%C A330282 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 A330282 Binomial transform of A330229.
%e A330282 The a(0) = 1 through a(2) = 5 set-systems:
%e A330282   {}  {}     {}
%e A330282       {{1}}  {{1}}
%e A330282              {{2}}
%e A330282              {{1},{1,2}}
%e A330282              {{2},{1,2}}
%t A330282 graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]],i},{i,Length[p]}])],{p,Permutations[Union@@m]}]];
%t A330282 Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],Length[graprms[#]]==Length[Union@@#]!&]],{n,0,3}]
%Y A330282 Costrict (or T_0) set-systems are A326940.
%Y A330282 The covering case is A330229.
%Y A330282 The unlabeled version is A330294, with covering case A330295.
%Y A330282 Achiral set-systems are A083323.
%Y A330282 BII-numbers of fully chiral set-systems are A330226.
%Y A330282 Non-isomorphic fully chiral multiset partitions are A330227.
%Y A330282 Fully chiral partitions are A330228.
%Y A330282 Fully chiral factorizations are A330235.
%Y A330282 MM-numbers of fully chiral multisets of multisets are A330236.
%Y A330282 Cf. A000612, A016031, A319637, A330098, A330231, A330232, A330234.
%K A330282 nonn,more
%O A330282 0,2
%A A330282 _Gus Wiseman_, Dec 10 2019