OFFSET
0,3
COMMENTS
A multiset partition is fully chiral if every permutation of the vertices gives a different representative. The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 16 multiset partitions:
{1} {11} {111} {1111}
{1}{1} {122} {1222}
{1}{11} {1}{111}
{1}{22} {11}{11}
{2}{12} {1}{122}
{1}{1}{1} {1}{222}
{1}{2}{2} {12}{22}
{1}{233}
{2}{122}
{1}{1}{11}
{1}{1}{22}
{1}{2}{22}
{1}{3}{23}
{2}{2}{12}
{1}{1}{1}{1}
{1}{2}{2}{2}
CROSSREFS
MM-numbers of these multiset partitions are the odd terms of A330236.
Non-isomorphic costrict (or T_0) multiset partitions are A316980.
Non-isomorphic achiral multiset partitions are A330223.
BII-numbers of fully chiral set-systems are A330226.
Fully chiral partitions are counted by A330228.
Fully chiral covering set-systems are A330229.
Fully chiral factorizations are A330235.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Dec 08 2019
STATUS
approved