0,5

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.

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.

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

a(n) = (1/5!)*([32]_n - 20*[24]_n + 60*[20]_n + 20*[18]_n + 10*[17]_n - 110*[16]_n - 120*[15]_n + 150*[14]_n + 120*[13]_n - 240*[12]_n + 20*[11]_n + 240*[10]_n + 40*[9]_n - 205*[8]_n + 60*[7]_n - 210*[6]_n + 210*[5]_n + 50*[4]_n - 100*[3]_n + 24*[2]_n), where [k]_n := k*(k - 1)*...*(k - n + 1), [k]_0 = 1.

Cf. A059079, A059080, A059082, A059083, A059048-A059052.

Sequence in context: A053293 A004817 A089535 this_sequence A056048 A051113 A067174

Adjacent sequences: A059078 A059079 A059080 this_sequence A059082 A059083 A059084

fini,nonn

Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Jan 06 2001