4 problems

For every $psilon>0$, there exists a constant $C_{psilon}<\infty$ such that, for every $n\ngreater than or equal to 1$ and every increasing set $A\not=\emptyset$ in ${0,1}^n$ satis…

Let $\Sigma$ be a finite alphabet, let $k\in\mathbb{N}$, and let $\mu$ be a pairwise-connected distribution over $\Sigma^k$ in which every atom has mass at least $\alpha$. A functi…

Let $p:\{-1,1\}^n\to\mathbb{R}$ be a polynomial of degree at most $d$. Its Fourier completely bounded $d$-norm is denoted by $\|p\|_{\operatorname{fcb},d}$, and…

Let $\rho$ satisfy $0\leq\rho\leq1$, let $b1\in[1,9]$, and let $\mathbf{MaxStab}_{\alpha}(1/2)$ denote the maximal asymmetric $b1$-stability at mean $1/2$. A dictator function is a…