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

1, 2, 5, 52, 21521

Offset: 0

Author

Gus Wiseman, Dec 10 2019

Keywords

• nonn
• more

Comments

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.

Examples

			The a(0) = 1 through a(2) = 5 set-systems:
  {}  {}     {}
      {{1}}  {{1}}
             {{2}}
             {{1},{1,2}}
             {{2},{1,2}}
		

Crossrefs

Costrict (or T_0) set-systems are A326940.

The covering case is A330229.

The unlabeled version is A330294, with covering case A330295.

Achiral set-systems are A083323.

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

Non-isomorphic fully chiral multiset partitions are A330227.

Fully chiral partitions are A330228.

Fully chiral factorizations are A330235.

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

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

Programs

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}]

Formula

Binomial transform of A330229.