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

1, 2, 5, 52, 21521

Offset

0,2

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.

Links

Table of n, a(n) for n=0..4.

Formula

Binomial transform of A330229.

Example

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

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}]

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.

Sequence in context: A206584 A268286 A081090 * A071880 A071882 A206848

Adjacent sequences: A330279 A330280 A330281 * A330283 A330284 A330285

Keyword

nonn,more

Author

Gus Wiseman, Dec 10 2019

Status

approved