|
|
A056163
|
|
Number of ordered antichains on an unlabeled n-set; labeled T_1-hypergraphs with n hyperedges.
|
|
1
|
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
hard,more,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|