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A056163
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Number of ordered antichains on an unlabeled n-set; labeled T_1-hypergraphs with n hyperedges.
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1
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OFFSET
| 0,1
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COMMENTS
| A T_1-hypergraph is a hypergraph (not necessarily without empty hyperedges or multiple hyperedges) which for every ordered pair of distinct nodes has a hyperedge containing one but not the other node.
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REFERENCES
| V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
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LINKS
| K. S. Brown, Dedekind's problem
Eric Weisstein's World of Mathematics, Antichain covers"
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FORMULA
| a(n)=Sum_{k=0..C(n, floor(n/2))}b(k, n) where b(k, n) is the number of k-element ordered antichains on an unlabeled n-set.
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EXAMPLE
| a(1)=1+2=3; a(2)=1+3+1=5; a(3)=1+4+4+2=11; a(4)=1+5+10+19+25+30+30=120; a(5)=1+6+20+90+454+2206+8340+20580+38640+60480+60480=191297.
There are 11 ordered antichains on an unlabeled 3-set: 0, (0), ({1}), ({1,2}), ({1,2,3}), ({1},{2}), ({1},{2,3}), ({2,3},{1}), ({1,2},{1,3}), ({1},{2},{3}), ({1,2},{1,3},{2,3}).
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CROSSREFS
| Cf. A000372 for (unordered) antichains on a labeled n-set, A056005, A056069-A056071, A056073, A056046-A056049, A056052, A056101, A056104, A051112-A051118.
Sequence in context: A088053 A050444 A117701 * A118573 A051835 A075883
Adjacent sequences: A056160 A056161 A056162 * A056164 A056165 A056166
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KEYWORD
| hard,more,nonn
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AUTHOR
| Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Jul 31 2000
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