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%I A014466
%S A014466 1,2,5,19,167,7580,7828353,2414682040997,56130437228687557907787
%N A014466 Dedekind numbers: monotone Boolean functions, or nonempty antichains 
               of subsets of an n-set
%C A014466 A monotone Boolean function is an increasing functions from P(S), the 
               set of subsets of S, to {0,1}.
%C A014466 The count of antichains includes the antichain consisting of only the 
               empty set, but excludes the empty antichain.
%C A014466 Also counts bases of hereditary systems.
%D A014466 I. Anderson, Combinatorics of Finite Sets. Oxford Univ. Press, 1987, 
               p. 38.
%D A014466 Arocha, Jorge Luis (1987) "Antichains in ordered sets" [ In Spanish ]. 
               Anales del Instituto de Matematicas de la Universidad Nacional Autonoma 
               de Mexico 27: 1-21.
%D A014466 J. Berman, ``Free spectra of 3-element algebras,'' in R. S. Freese and 
               O. C. Garcia, editors, Universal Algebra and Lattice Theory (Puebla, 
               1982), Lect. Notes Math. Vol. 1004, 1983.
%D A014466 G. Birkhoff, Lattice Theory. American Mathematical Society, Colloquium 
               Publications, Vol. 25, 3rd ed., Providence, RI, 1967, p. 63.
%D A014466 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 273.
%D A014466 J. Dezert, Fondations pour une nouvelle theorie du raisonnement plausible 
               et paradoxal (la DSmT), Tech. Rep. 1/06769 DTIM, ONERA, Paris, page 
               33, January 2003.
%D A014466 J. Dezert, F. Smarandache, On the generating of hyper-powersets for the 
               DSmT, Proceedings of the 6th International Conference on Information 
               Fusion, Cairns, Australia, 2003.
%D A014466 M. A. Harrison, Introduction to Switching and Automata Theory. McGraw 
               Hill, NY, 1965, p. 188.
%D A014466 D. J. Kleitman, On Dedekind's problem: The number of monotone Boolean 
               functions. Proc. Amer. Math. Soc. 21 1969 677-682.
%D A014466 D. J. Kleitman and G. Markowsky, On Dedekind's problem: the number of 
               isotone Boolean functions. II. Trans. Amer. Math. Soc. 213 (1975), 
               373-390.
%D A014466 W. F. Lunnon, The IU function: the size of a free distributive lattice, 
               pp. 173-181 of D. J. A. Welsh, editor, Combinatorial Mathematics 
               and Its Applications. Academic Press, NY, 1971.
%D A014466 S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 
               38 and 214.
%D A014466 F. Smarandache (editor), Proceedings of the First International Conference 
               on Neutrosophics, University of New Mexico, 1-3 December 2001, Xiquan, 
               2002.
%D A014466 D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 
               2001, p. 349.
%D A014466 D. H. Wiedemann, A computation of the eighth Dedekind number, Order 8 
               (1991) 5-6.
%H A014466 K. Atanassov, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">
               On Some of Smarandache's Problems</a>
%H A014466 K. S. Brown, <a href="http://www.mathpages.com/home/kmath030.htm">Dedekind's 
               problem</a>
%H A014466 J. Dezert, <a href="http://www.gallup.unm.edu/~smarandache/IS2002Sept24.pdf">
               Foundations for a new theory for plausible and paradoxical reasoning</
               a>, Tech. Rep. DTIM/IED, ONERA, Paris, pp. 14-15, 2002.
%H A014466 J. L. King, <a href="http://www.math.ufl.edu/~squash/">Brick tiling and 
               monotone Boolean functions</a>
%H A014466 F. Smarandache (editor), <a href="http://www.gallup.unm.edu/~smarandache/
               NeutrosophicProceedings.pdf">Proceedings of the First International 
               Conference on Neutrosophics</a>.
%H A014466 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Antichain.html">Link to a section of The World of Mathematics.</a>
%H A014466 <a href="Sindx_Bo.html#Boolean">Index entries for sequences related to 
               Boolean functions</a>
%e A014466 a(2)=5 from the antichains {{}}, {{1}}, {{2}}, {{1,2}}, {{1},{2}}.
%Y A014466 Equals A000372 - 1 = A007153 + 1. Cf. A003182.
%Y A014466 Sequence in context: A054926 A002786 A039719 this_sequence A108799 A085871 
               A080280
%Y A014466 Adjacent sequences: A014463 A014464 A014465 this_sequence A014467 A014468 
               A014469
%K A014466 nonn,hard,nice
%O A014466 0,2
%A A014466 N. J. A. Sloane (njas(AT)research.att.com).
%E A014466 Last term from D. H. Wiedemann, personal communication.
%E A014466 Additional comments from Michael Somos, Jun 10 2002.

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