2 problems

Fix $0<delta<1$ and $epsilon>0$. For each $k\in\mathbb{N}$, let $Emb(1+epsilon,k,delta)$ denote the least dimension $N$ such that every subset of $\{0,1\}^N$ of density at least…

Fix $k\in\mathbb{N}$ and $0<delta<1$. Let $Emb(1,delta,k)$ be the smallest $N$ such that every subset $\mathcal{D}\subset\{0,1\}^N$ of density at least $delta$ contains the image o…