A059080 Triangle A(n,m) of numbers of n-element T_0-antichains on a labeled m-set, m=0,...,2^n.

1, 1, 1, 2, 2, 0, 0, 1, 6, 12, 0, 0, 0, 2, 52, 520, 2640, 6720, 6720, 0, 0, 0, 0, 25, 1770, 53940, 1012620, 13487040, 136745280, 1094688000, 7025356800, 36084787200, 145297152000, 435891456000, 871782912000, 871782912000

Offset

0,4

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. Row sums give A059079. Column sums give A059083.

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

Table of n, a(n) for n=0..35.

V. Jovovic, 3-element T_0-antichains on a labeled 4-set

V. Jovovic, Formula for the number of m-element T_0-antichains on a labeled n-set

Example

[1, 1], [1, 2, 2], [0, 0, 1, 6, 12], [0, 0, 0, 2, 52, 520, 2640, 6720, 6720], ...; there are 2 3-element T_0-antichains on a 3-set: {{1}, {2}, {3}}, {{1, 2}, {1, 3}, {2, 3}}.

Crossrefs

Cf. A059079, A059081-A059083, A059048-A059052.

Sequence in context: A125226 A281790 A245254 * A062070 A347088 A343991

Adjacent sequences: A059077 A059078 A059079 * A059081 A059082 A059083

Keyword

nonn

Author

Vladeta Jovovic, Goran Kilibarda, Dec 29 2000

Status

approved