A330295
Number of non-isomorphic fully chiral set-systems covering n vertices.
Original entry on oeis.org
1, 1, 1, 7, 889
Offset: 0
Non-isomorphic representatives of the a(0) = 1 through a(3) = 7 set-systems:
0 {1} {1}{12} {1}{2}{13}
{1}{12}{23}
{1}{12}{123}
{1}{2}{12}{13}
{1}{2}{13}{123}
{1}{12}{23}{123}
{1}{2}{12}{13}{123}
First differences of
A330294 (the non-covering case).
Unlabeled costrict (or T_0) set-systems are
A326946.
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,
A055621,
A083323,
A283877,
A319637,
A330098,
A330231,
A330232,
A330234,
A330282.
A330343
Number of labeled fully chiral simple graphs (also called identity or asymmetric graphs) covering n vertices.
Original entry on oeis.org
1, 0, 0, 0, 0, 5760, 766080, 149022720, 48990251520, 28928242022400, 32147584690636800, 69035206021583155200
Offset: 1
Covering simple graphs are
A006129.
Full chiral integer partitions are
A330228.
Fully chiral factorizations are
A330235.
Cf.
A006125,
A016031,
A124059,
A143543,
A330098,
A330224,
A330226,
A330227,
A330230,
A330231,
A330236.
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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],{2}]],Length[graprms[#]]==n!&]],{n,5}] (* brute force, not for computation *)
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