Monte Carlo methods (pair matching, reference subsets, weight-layer branching) give D(10)≈8.93×10^78 through D(15)≈3.81×10^1953 with explicit standard errors, beating Korshunov asymptotics.
On the number of inequivalent monotone Boolean functions of 8 variables
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abstract
In this paper, the author presents algorithms that allow determining the number of fixed points in permutations of a set of monotone Boolean functions. Then, using Burnside's lemma, the author determines the number of inequivalent monotone Boolean functions of 8 variables. The number obtained is 1,392,195,548,889,993,358.
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2026 1verdicts
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Statistical Estimation of higher Dedekind Numbers
Monte Carlo methods (pair matching, reference subsets, weight-layer branching) give D(10)≈8.93×10^78 through D(15)≈3.81×10^1953 with explicit standard errors, beating Korshunov asymptotics.