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A330282 Number of fully chiral set-systems on n vertices. 6
1, 2, 5, 52, 21521 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A206584 A268286 A081090 * A071880 A071882 A206848
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Dec 10 2019
STATUS
approved

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Last modified May 24 07:02 EDT 2024. Contains 372772 sequences. (Running on oeis4.)