A330227 - OEIS

%I #7 Dec 08 2019 20:55:10

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

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

%C 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.

%e Non-isomorphic representatives of the a(1) = 1 through a(4) = 16 multiset partitions:

%e   {1}  {11}    {111}      {1111}

%e        {1}{1}  {122}      {1222}

%e                {1}{11}    {1}{111}

%e                {1}{22}    {11}{11}

%e                {2}{12}    {1}{122}

%e                {1}{1}{1}  {1}{222}

%e                {1}{2}{2}  {12}{22}

%e                           {1}{233}

%e                           {2}{122}

%e                           {1}{1}{11}

%e                           {1}{1}{22}

%e                           {1}{2}{22}

%e                           {1}{3}{23}

%e                           {2}{2}{12}

%e                           {1}{1}{1}{1}

%e                           {1}{2}{2}{2}

%Y MM-numbers of these multiset partitions are the odd terms of A330236.

%Y Non-isomorphic costrict (or T_0) multiset partitions are A316980.

%Y Non-isomorphic achiral multiset partitions are A330223.

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

%Y Fully chiral partitions are counted by A330228.

%Y Fully chiral covering set-systems are A330229.

%Y Fully chiral factorizations are A330235.

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

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Dec 08 2019