cp's OEIS Frontend

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

%I A330227 #7 Dec 08 2019 20:55:10
%S A330227 1,1,2,7,16,49,144,447,1417,4707
%N A330227 Number of non-isomorphic fully chiral multiset partitions of weight n.
%C A330227 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 A330227 Non-isomorphic representatives of the a(1) = 1 through a(4) = 16 multiset partitions:
%e A330227   {1}  {11}    {111}      {1111}
%e A330227        {1}{1}  {122}      {1222}
%e A330227                {1}{11}    {1}{111}
%e A330227                {1}{22}    {11}{11}
%e A330227                {2}{12}    {1}{122}
%e A330227                {1}{1}{1}  {1}{222}
%e A330227                {1}{2}{2}  {12}{22}
%e A330227                           {1}{233}
%e A330227                           {2}{122}
%e A330227                           {1}{1}{11}
%e A330227                           {1}{1}{22}
%e A330227                           {1}{2}{22}
%e A330227                           {1}{3}{23}
%e A330227                           {2}{2}{12}
%e A330227                           {1}{1}{1}{1}
%e A330227                           {1}{2}{2}{2}
%Y A330227 MM-numbers of these multiset partitions are the odd terms of A330236.
%Y A330227 Non-isomorphic costrict (or T_0) multiset partitions are A316980.
%Y A330227 Non-isomorphic achiral multiset partitions are A330223.
%Y A330227 BII-numbers of fully chiral set-systems are A330226.
%Y A330227 Fully chiral partitions are counted by A330228.
%Y A330227 Fully chiral covering set-systems are A330229.
%Y A330227 Fully chiral factorizations are A330235.
%Y A330227 Cf. A000612, A001055, A007716, A055621, A283877, A317533, A322847, A330098, A330232.
%K A330227 nonn,more
%O A330227 0,3
%A A330227 _Gus Wiseman_, Dec 08 2019