A056164 - OEIS

%I #11 Jun 17 2013 03:32:12

%S 1,2,6,109,191177

%N Number of ordered antichain covers of an unlabeled n-set; labeled T_1-hypergraphs (without empty hyperedges) with n hyperedges.

%C 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.

%D 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)

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

%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath515.htm">Dedekind's problem</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cover.html">Antichain covers</a>

%F a(n)=Sum_{k=1..C(n, floor(n/2))}b(k, n) where b(k, n) is the number of k-element ordered antichains covers of an unlabeled n-set.

%e There are 6 ordered antichain covers on an unlabeled 3-set: ({1,2,3}), ({1},{2,3}), ({2,3},{1}), ({1,2},{1,3}), ({1},{2},{3}), ({1,2},{1,3},{2,3}).

%e a(3)=1+3+2=6; a(4)=1+6+17+25+30+30=109; a(5)=1+10+71+429+2176+8310+20580+38640+60480+60480=191177.

%Y Cf. A056074, A056090, A056093, A000372, A056005, A056069-A056071, A056073, A056046-A056049, A056052, A056101, A056104, A051112-A051118.

%K hard,more,nonn

%O 1,2

%A _Vladeta Jovovic_, Goran Kilibarda, Jul 31 2000