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A003182 Dedekind numbers: inequivalent monotone Boolean functions of n or fewer variables, or antichains of subsets of an n-set.
(Formerly M0729)
+0
8
2, 3, 5, 10, 30, 210, 16353 (list; graph; listen)
OFFSET

0,1

COMMENT

NP-equivalence classes of unate Boolean functions of n or fewer variables.

REFERENCES

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.

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 I. 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, Table 2.3.2. - Row 13.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

D. H. Wiedemann, personal communication.

LINKS

K. S. Brown, Dedekind's problem

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

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

Index entries for sequences related to Boolean functions

CROSSREFS

Cf. A000372, A007153.

Sequence in context: A000617 A132183 A003504 this_sequence A134294 A154956 A130165

Adjacent sequences: A003179 A003180 A003181 this_sequence A003183 A003184 A003185

KEYWORD

nonn,hard,nice

AUTHOR

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

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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