A327060 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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.

LINKS

Table of n, a(n) for n=0..10.

EXAMPLE

Non-isomorphic representatives of the a(0) = 1 through a(5) = 11 multiset partitions:

{} {{1}} {{11}} {{111}} {{1111}} {{11111}}

{{1}{1}} {{123}} {{1222}} {{12222}}

{{1}{1}{1}} {{1233}} {{12233}}

{{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.

Sequence in context: A054075 A366753 A062798 * A270817 A182828 A294229

Adjacent sequences: A327057 A327058 A327059 * A327061 A327062 A327063

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 18 2019

STATUS

approved