login
Number of non-isomorphic fully chiral set-systems on n vertices.
5

%I #11 Jan 05 2020 12:03:02

%S 1,2,3,10,899

%N Number of non-isomorphic fully chiral set-systems on n vertices.

%C 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.

%e Non-isomorphic representatives of the a(0) = 1 through a(3) = 10 set-systems:

%e 0 0 0 0

%e {1} {1} {1}

%e {2}{12} {2}{12}

%e {1}{3}{23}

%e {2}{13}{23}

%e {3}{23}{123}

%e {2}{3}{13}{23}

%e {1}{3}{23}{123}

%e {2}{13}{23}{123}

%e {2}{3}{13}{23}{123}

%Y The labeled version is A330282.

%Y Partial sums of A330295 (the covering case).

%Y Unlabeled costrict (or T_0) set-systems are A326946.

%Y BII-numbers of fully chiral set-systems are A330226.

%Y Non-isomorphic fully chiral multiset partitions are A330227.

%Y Fully chiral partitions are A330228.

%Y Fully chiral factorizations are A330235.

%Y MM-numbers of fully chiral multisets of multisets are A330236.

%Y Cf. A000612, A016031, A055621, A083323, A283877, A319637, A330098, A330231, A330232, A330234.

%K nonn,more

%O 0,2

%A _Gus Wiseman_, Dec 10 2019