A330227 Number of non-isomorphic fully chiral multiset partitions of weight n.

1, 1, 2, 7, 16, 49, 144, 447, 1417, 4707

Offset: 0

Author

Gus Wiseman, Dec 08 2019

Keywords

• nonn
• more

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.

Examples

			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.

Cf. A000612, A001055, A007716, A055621, A283877, A317533, A322847, A330098, A330232.