A319645 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is a chain of distinct multisets.

1, 1, 1, 2, 3, 4, 7, 9, 16, 22, 38

Offset: 0

Author

Gus Wiseman, Sep 25 2018

Keywords

• nonn
• more

Comments

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

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(6) = 7 antichains:
1: {{1}}
2: {{1,1}}
3: {{1,1,1}}
   {{1,2,2}}
4: {{1,1,1,1}}
   {{1,2,2,2}}
   {{1,2},{2,2}}
5: {{1,1,1,1,1}}
   {{1,1,2,2,2}}
   {{1,2,2,2,2}}
   {{1,2},{2,2,2}}
6: {{1,1,1,1,1,1}}
   {{1,1,2,2,2,2}}
   {{1,2,2,2,2,2}}
   {{1,2,2,3,3,3}}
   {{1,2},{2,2,2,2}}
   {{1,2,2},{2,2,2}}
   {{1,2,3},{2,3,3}}
		

Crossrefs

Cf. A000219, A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319616-A319646.