3 problems

For each $n$, let $X=\mathbb{F}_2^n$ and $N=|X|=2^n$. Let $r=(r_x)_{x\in X}$ be a fixed table of $n$-bit strings, and define $f_{h,r}:X\to X\times X\times\{0,1\}^n$ by…

Let $B_N$ be the hyperoctahedral group and let $V=V_{((N-1),(1))}$ be its natural representation. Let $T(B_N,V)$ be the tensor product graph, let $I(V)$ denote its identity represe…

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…