A327060 Number of non-isomorphic weight-n weak antichains of multisets where every two vertices appear together in some edge (cointersecting).

1, 1, 3, 4, 9, 11, 30, 42, 103, 194, 443

Offset: 0

Author

Gus Wiseman, Aug 18 2019

Keywords

• nonn
• more

Comments

A multiset partition is a finite multiset of finite nonempty multisets. It is a weak antichain if no part is a proper submultiset of any other.

Examples

			Non-isomorphic representatives of the a(0) = 1 through a(5) = 11 multiset partitions:
  {}  {{1}}  {{11}}    {{111}}      {{1111}}        {{11111}}
             {{12}}    {{122}}      {{1122}}        {{11222}}
             {{1}{1}}  {{123}}      {{1222}}        {{12222}}
                       {{1}{1}{1}}  {{1233}}        {{12233}}
                                    {{1234}}        {{12333}}
                                    {{11}{11}}      {{12344}}
                                    {{12}{12}}      {{12345}}
                                    {{12}{22}}      {{11}{122}}
                                    {{1}{1}{1}{1}}  {{12}{222}}
                                                    {{33}{123}}
                                                    {{1}{1}{1}{1}{1}}
		

Crossrefs

Antichains are A000372.

The BII-numbers of these set-systems are the intersection of A326853 and A326704.

Cointersecting set-systems are A327039.

The set-system version is A327057, with covering case A327058.

Cf. A006126, A007716, A051185, A305844, A326965, A327020, A327059, A327062.