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A dimension-free comparison between expectation thresholds and fractional expectation thresholds
We prove a dimension-free comparison between the expectation threshold $q(\mathcal F)$ and the fractional expectation threshold $q_f(\mathcal F)$ for any nontrivial increasing family $\mathcal F$ on a finite ground set. Specifically, we show that there is a universal constant $K>0$ such that \[ q_f(
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