A059083 - OEIS

%I #13 Mar 22 2020 17:13:48

%S 2,3,3,8,96,6373,7725703,2414518872815,56130437161078967568912

%N Number of T_0-antichains on a labeled n-set.

%C 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.

%D V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

%H V. Jovovic, <a href="/A059080/a059080.pdf">3-element T_0-antichains on a labeled 4-set</a>

%H V. Jovovic, <a href="/A059083/a059083.pdf">Formula for the number of m-element T_0-antichains on a labeled n-set</a>

%H V. Jovovic, G. Kilibarda, <a href="http://www.mathnet.ru/php/archive.phtml?wshow=paper&amp;jrnid=dm&amp;paperid=398&amp;option_lang=eng">On the number of Boolean functions in the Post classes F^{mu}_8</a>, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).

%F a(n) = Sum_{m=0..binomial(n, floor(n/2))} A(m, n), where A(m, n) is number of m-element T_0-antichains on a labeled n-set. Cf. A059080.

%F a(n) = column sums of A059080.

%e a(0) = 1 + 1, a(1) = 1 + 2, a(2) = 2 + 1, a(3) = 6 + 2, a(4) = 12 + 52 + 25 + 6 + 1, a(5) = 520 + 1770 + 2086 + 1370 + 490 + 115 + 20 + 2.

%Y Cf. A059079-A059082, A059048-A059052.

%Y Cf. A000372.

%K hard,nonn

%O 0,1

%A _Vladeta Jovovic_, Goran Kilibarda, Jan 06 2001

%E More terms from _Vladeta Jovovic_, Nov 28 2003