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A319641
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Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of (not necessarily distinct) multisets.
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1
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1, 1, 3, 5, 11, 18, 41, 70, 159, 323, 778
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OFFSET
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0,3
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COMMENTS
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The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks 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.
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LINKS
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FORMULA
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EXAMPLE
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Non-isomorphic representatives of the a(1) = 1 through a(4) = 11 antichains:
1: {{1}}
2: {{1,1}}
{{1,2}}
{{1},{2}}
3: {{1,1,1}}
{{1,2,3}}
{{1},{2,2}}
{{1},{2,3}}
{{1},{2},{3}}
4: {{1,1,1,1}}
{{1,1,2,2}}
{{1,2,3,4}}
{{1},{2,2,2}}
{{1},{2,3,4}}
{{1,1},{2,2}}
{{1,2},{3,3}}
{{1,2},{3,4}}
{{1},{2},{3,3}}
{{1},{2},{3,4}}
{{1},{2},{3},{4}}
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CROSSREFS
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Cf. A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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