Search: id:A046873
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%I A046873
%S A046873 1,1,2,48,1680384,14807804035657359360
%N A046873 Number of total orders extending inclusion on P({1,...,n}).
%C A046873 Trivial upper bound: a(n)<=(2^n)!
%C A046873 Number of linear extensions of the boolean lattice 2^n. - Mitch Harris 
               (Harris.Mitchell (AT) mgh.harvard.edu), Dec 27, 2005
%C A046873 The number of vertices in the representation of all linear extensions 
               in a distributive lattice are the Dedekind numbers (A000372) and 
               the number of edges constitutes A118077. - Oliver W. Wienand (wienand(AT)mathematik.uni-kl.de), 
               Apr 11 2006, using Python and an inference method for computing the 
               set of linear extensions of arbitrary posets.
%D A046873 Brightwell, Graham R. and Tetali, Prasad, The number of linear extensions 
               of the Boolean lattice, Order, v. 20 (2003), no.4, 333-345. (Gives 
               asymptotics).
%D A046873 Sha, Ji Chang and Kleitman, D. J., The number of linear extensions of 
               subset ordering. Discrete Math. 63 (1987), no. 2-3, 271-278.
%e A046873 a(2)=2 because either {}<{0}<{1}<{0,1} or {}<{1}<{0}<{0,1}
%Y A046873 Cf. A001206, A114717, A000372, A118077.
%Y A046873 Sequence in context: A057527 A166475 A152688 this_sequence A164334 A100540 
               A138076
%Y A046873 Adjacent sequences: A046870 A046871 A046872 this_sequence A046874 A046875 
               A046876
%K A046873 nonn,nice
%O A046873 0,3
%A A046873 David A. Madore (david.madore(AT)ens.fr)
%E A046873 a(5) from Oliver W. Wienand (wienand(AT)mathematik.uni-kl.de), Apr 11 
               2006, using Python and an inference method for computing the set 
               of linear extensions of arbitrary posets.

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