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A046873
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Number of total orders extending inclusion on P({1,...,n}).
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1
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OFFSET
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0,3
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=0..6.
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EXAMPLE
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a(2)=2 because either {}<{0}<{1}<{0,1} or {}<{1}<{0}<{0,1}
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CROSSREFS
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Cf. A001206, A114717, A000372, A118077.
Sequence in context: A057527 A166475 A152688 * A164334 A100540 A007861
Adjacent sequences: A046870 A046871 A046872 * A046874 A046875 A046876
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KEYWORD
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nonn,nice
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AUTHOR
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David A. Madore (david.madore(AT)ens.fr)
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EXTENSIONS
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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.
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STATUS
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approved
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