2 problems

Mansour's conjecture. For every $\boldsymbol{\rho}>0$, the Fourier spectrum of $f$ is $\boldsymbol{\rho}$-concentrated on a collection of at most $\operatorname{poly}(n)$ character…

Let $f\colon\left\{0,1\right\}^{n}\to\left\{0,1\right\}$ be a monotone Boolean function with expectation $\mathbb{E}[f]=\mu$, and let $I[f]$ denote its total influence. A DNF of wi…