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A319779
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Number of intersecting multiset partitions of weight n whose dual is not an intersecting multiset partition.
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16
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1, 0, 0, 0, 1, 4, 20, 66, 226, 696, 2156
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OFFSET
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0,6
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COMMENTS
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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 weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.
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LINKS
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Table of n, a(n) for n=0..10.
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EXAMPLE
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Non-isomorphic representatives of the a(4) = 1 through a(6) = 20 multiset partitions:
4: {{1,3},{2,3}}
5: {{1,2},{2,3,3}}
{{1,3},{2,3,3}}
{{1,4},{2,3,4}}
{{3},{1,3},{2,3}}
6: {{1,2},{2,3,3,3}}
{{1,3},{2,2,3,3}}
{{1,3},{2,3,3,3}}
{{1,3},{2,3,4,4}}
{{1,4},{2,3,4,4}}
{{1,5},{2,3,4,5}}
{{1,1,2},{2,3,3}}
{{1,2,2},{2,3,3}}
{{1,2,3},{3,4,4}}
{{1,2,4},{3,4,4}}
{{1,2,5},{3,4,5}}
{{1,3,3},{2,3,3}}
{{1,3,4},{2,3,4}}
{{2},{1,2},{2,3,3}}
{{3},{1,3},{2,3,3}}
{{4},{1,4},{2,3,4}}
{{1,3},{2,3},{2,3}}
{{1,3},{2,3},{3,3}}
{{1,4},{2,4},{3,4}}
{{3},{3},{1,3},{2,3}}
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CROSSREFS
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Cf. A007716, A281116, A283877, A305854, A306006, A316980, A316983, A317757, A319616.
Cf. A319775, A319778, A319781, A319783.
Sequence in context: A194094 A055538 A302317 * A287244 A344993 A123613
Adjacent sequences: A319776 A319777 A319778 * A319780 A319781 A319782
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KEYWORD
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nonn,more
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AUTHOR
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Gus Wiseman, Sep 27 2018
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STATUS
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approved
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