This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A046873 Number of total orders extending inclusion on P({1,...,n}). 1
 1, 1, 2, 48, 1680384, 14807804035657359360, 141377911697227887117195970316200795630205476957716480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Trivial upper bound: a(n)<=(2^n)! Number of linear extensions of the boolean lattice 2^n. - Mitch Harris, Dec 27, 2005 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 Wienand, Apr 11 2006, using Python and an inference method for computing the set of linear extensions of arbitrary posets. REFERENCES 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). Sha, Ji Chang and Kleitman, D. J., The number of linear extensions of subset ordering. Discrete Math. 63 (1987), no. 2-3, 271-278. LINKS EXAMPLE a(2)=2 because either {}<{0}<{1}<{0,1} or {}<{1}<{0}<{0,1} CROSSREFS Cf. A001206, A114717, A000372, A118077. Sequence in context: A057527 A166475 A152688 * A164334 A100540 A007861 Adjacent sequences:  A046870 A046871 A046872 * A046874 A046875 A046876 KEYWORD nonn,nice AUTHOR David A. Madore (david.madore(AT)ens.fr) EXTENSIONS a(5) from Oliver Wienand, Apr 11 2006, using Python and an inference method for computing the set of linear extensions of arbitrary posets. Using the same method on a compute server generated a(6) on Dec 5 2010. STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .