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 9 variables
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abstract
We provide the first-ever calculation of the number of inequivalent monotone Boolean functions of 9 variables, which is equal to 789,204,635,842,035,040,527,740,846,300,252,680.
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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.