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A056163
Number of ordered antichains on an unlabeled n-set; labeled T_1-hypergraphs with n hyperedges.
1
2, 3, 5, 11, 120, 191297
OFFSET
0,1
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.
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.
LINKS
K. S. Brown, Dedekind's problem
Eric Weisstein's World of Mathematics, Antichain covers
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.
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}).
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
KEYWORD
hard,more,nonn
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Jul 31 2000
STATUS
approved