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A319778 Number of non-isomorphic set systems of weight n with empty intersection whose dual is also a set system with empty intersection. 12
1, 0, 1, 1, 2, 5, 13, 28, 72, 181, 483 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. The dual of a multiset partition has empty intersection iff no part contains all the vertices.

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

LINKS

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

EXAMPLE

Non-isomorphic representatives of the a(2) = 1 through a(6) = 13 multiset partitions:

2: {{1},{2}}

3: {{1},{2},{3}}

4: {{1},{3},{2,3}}

   {{1},{2},{3},{4}}

5: {{1},{2,4},{3,4}}

   {{2},{1,3},{2,3}}

   {{1},{2},{3},{2,3}}

   {{1},{2},{4},{3,4}}

   {{1},{2},{3},{4},{5}}

6: {{3},{1,4},{2,3,4}}

   {{1,2},{1,3},{2,3}}

   {{1,3},{2,4},{3,4}}

   {{1},{2},{1,3},{2,3}}

   {{1},{2},{3,5},{4,5}}

   {{1},{3},{4},{2,3,4}}

   {{1},{3},{2,4},{3,4}}

   {{1},{4},{2,4},{3,4}}

   {{2},{3},{1,3},{2,3}}

   {{2},{4},{1,2},{3,4}}

   {{1},{2},{3},{4},{3,4}}

   {{1},{2},{3},{5},{4,5}}

   {{1},{2},{3},{4},{5},{6}}

CROSSREFS

Cf. A007716, A049311, A281116, A283877, A316980, A317752, A317755, A317757.

Cf. A319775, A319779, A319781, A319783.

Sequence in context: A320933 A290194 A241392 * A002559 A049097 A045366

Adjacent sequences:  A319775 A319776 A319777 * A319779 A319780 A319781

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 27 2018

STATUS

approved

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Last modified June 20 00:47 EDT 2019. Contains 324223 sequences. (Running on oeis4.)