A059048 Triangle A(n,m) of numbers of n-element ordered T_0-antichains on an unlabeled m-set or numbers of T_1-hypergraphs on n labeled nodes with m (not necessarily empty) distinct hyperedges (m=0,1,...,2^n).

1, 1, 1, 2, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 13, 26, 22, 8, 1, 0, 0, 0, 0, 25, 354, 1798, 4822, 8028, 9044, 7240, 4224, 1808, 560, 120, 16, 1, 0, 0, 0, 0, 30, 2086, 45512, 461236, 2797785, 11669660, 36369970, 89356260, 179461250, 302225100, 43458923, 0

Offset: 0

Author

Vladeta Jovovic, Goran Kilibarda, Dec 19 2000

Keywords

• nonn

Comments

An antichain on a set is a T_0-antichain if for every two distinct points of the set there exists a member of the antichain containing one but not the other point. T_1-hypergraph is a hypergraph which for every ordered pair (u,v) of distinct nodes has a hyperedge containing u but not v.

Examples

			[1, 1], [1, 2, 1], [0, 0, 1, 2, 1], [0, 0, 0, 2, 13, 26, 22, 8, 1], .... There are 72 3-element unlabeled ordered T_0-antichains: 2 on 3-set, 13 on 4-set, 26 on 5-set, 22 on 6-set, 8 on 7-set and 1 on 8-set.
		

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

• V. Jovovic, 3-element unlabeled ordered T_0-antichains"
• V. Jovovic, Number A(m,n) of m-element ordered T_0-antichains on an unlabeled n-set

Crossrefs

Cf. A059049-A059052.