|
%I #6 Oct 26 2018 12:50:18
%S 1,1,2,3,5,5,13,11,25,31,54
%N Number of non-isomorphic weight-n antichains of multisets whose dual is a chain of distinct multisets.
%C The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.
%C 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(5) = 5 antichains:
%e 1: {{1}}
%e 2: {{1,1}}
%e {{1},{1}}
%e 3: {{1,1,1}}
%e {{1,2,2}}
%e {{1},{1},{1}}
%e 4: {{1,1,1,1}}
%e {{1,2,2,2}}
%e {{1,1},{1,1}}
%e {{1,2},{2,2}}
%e {{1},{1},{1},{1}}
%e 5: {{1,1,1,1,1}}
%e {{1,1,2,2,2}}
%e {{1,2,2,2,2}}
%e {{1,2},{2,2,2}}
%e {{1},{1},{1},{1},{1}}
%Y Cf. A000219, A006126, A007716, A059201, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Sep 25 2018
|
