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A319634
Number of non-isomorphic antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily distinct) sets.
0
1, 1, 2, 4, 12, 87
OFFSET
0,3
COMMENTS
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}}.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 12 antichain covers:
{{1}} {{1,2}} {{1,2,3}} {{1,2,3,4}}
{{1},{2}} {{1},{2,3}} {{1},{2,3,4}}
{{1},{2},{3}} {{1,2},{3,4}}
{{1,2},{1,3},{2,3}} {{1},{2},{3,4}}
{{1},{2},{3},{4}}
{{1,2},{1,3,4},{2,3,4}}
{{1},{2,3},{2,4},{3,4}}
{{1,2},{1,3},{2,4},{3,4}}
{{1,2},{1,3},{1,4},{2,3,4}}
{{1,3},{1,4},{2,3},{2,4},{3,4}}
{{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
{{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 25 2018
STATUS
approved