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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 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

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