0,2

A monotone Boolean function is an increasing functions from P(S), the set of subsets of S, to {0,1}.

The count of antichains includes the antichain consisting of only the empty set, but excludes the empty antichain.

Also counts bases of hereditary systems.

I. Anderson, Combinatorics of Finite Sets. Oxford Univ. Press, 1987, p. 38.

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.

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.

G. Birkhoff, Lattice Theory. American Mathematical Society, Colloquium Publications, Vol. 25, 3rd ed., Providence, RI, 1967, p. 63.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 273.

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.

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.

M. A. Harrison, Introduction to Switching and Automata Theory. McGraw Hill, NY, 1965, p. 188.

D. J. Kleitman, On Dedekind's problem: The number of monotone Boolean functions. Proc. Amer. Math. Soc. 21 1969 677-682.

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.

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.

S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38 and 214.

F. Smarandache (editor), Proceedings of the First International Conference on Neutrosophics, University of New Mexico, 1-3 December 2001, Xiquan, 2002.

D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 349.

D. H. Wiedemann, A computation of the eighth Dedekind number, Order 8 (1991) 5-6.

K. Atanassov, On Some of Smarandache's Problems

K. S. Brown, Dedekind's problem

J. Dezert, Foundations for a new theory for plausible and paradoxical reasoning, Tech. Rep. DTIM/IED, ONERA, Paris, pp. 14-15, 2002.

J. L. King, Brick tiling and monotone Boolean functions

F. Smarandache (editor), Proceedings of the First International Conference on Neutrosophics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to Boolean functions

a(2)=5 from the antichains {{}}, {{1}}, {{2}}, {{1,2}}, {{1},{2}}.

Equals A000372 - 1 = A007153 + 1. Cf. A003182.

Sequence in context: A054926 A002786 A039719 this_sequence A108799 A085871 A080280

Adjacent sequences: A014463 A014464 A014465 this_sequence A014467 A014468 A014469

nonn,hard,nice

N. J. A. Sloane (njas(AT)research.att.com).

Last term from D. H. Wiedemann, personal communication.

Additional comments from Michael Somos, Jun 10 2002.