Gotsman-Linial Conjecture

Computational investigation: Is Inf[f] ≤ O(sqrt(n) · sdeg(f)) for all Boolean functions?

56
Functions Tested
100%
Conjecture Holds
0.866
Max Ratio
0.422
Mean Ratio

Summary Statistics for Inf[f] / (sqrt(n) * sdeg(f))

StatisticValue
Total Functions56
Max Ratio0.866
Mean Ratio0.422
Median Ratio0.433
Std Deviation0.196
95th Percentile0.830
Fraction Below 1100%

Ratio by Function Family

Ratio Distribution

Influence vs sqrt(n)*sdeg(f)

Max Ratio by Dimension