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Dedekind's Problem


The determination of the number of monotone Boolean functions of n variables (equivalent to the number of antichains on the n-set {1,2,...,n}) is called Dedekind's problem, and the numbers themselves are known as Dedekind numbers.


See also

Antichain, Boolean Function, Dedekind Number

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References

Dedekind, R. "Über Zerlegungen von Zahlen durch ihre grössten gemeinsammen Teiler." In Gesammelte Werke, Bd. 1. (Ed. K. May). Heidelberg, Germany: Mohr Siebeck, pp. 103-148, 1897.Jäkel, C. "A Computation of the Ninth Dedekind Number." 3 Apr 2023. https://arxiv.org/abs/2304.00895.Kleitman, D. "On Dedekind's Problem: The Number of Monotone Boolean Functions." Proc. Amer. Math. Soc. 21, 677-682, 1969.Kleitman, D. and Markowsky, G. "On Dedekind's Problem: The Number of Isotone Boolean Functions. II." Trans. Amer. Math. Soc. 213, 373-390, 1975.

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Dedekind's Problem

Cite this as:

Weisstein, Eric W. "Dedekind's Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DedekindsProblem.html

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