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A330343
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Number of labeled fully chiral simple graphs (also called identity or asymmetric graphs) covering n vertices.
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3
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1, 0, 0, 0, 0, 5760, 766080, 149022720, 48990251520, 28928242022400, 32147584690636800, 69035206021583155200
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OFFSET
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1,6
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COMMENTS
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In a fully chiral graph, every permutation of the vertices gives a different representative, so the only automorphism is the identity.
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LINKS
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FORMULA
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MATHEMATICA
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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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CROSSREFS
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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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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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