3 problems

Let $[n]=\{0,1,\ldots,n-1\}$, and let $c_d$ be the limiting density of a largest sum-free subset of $[n+1]^d$. For $u\in[0,d]$, define … and let $u_d^*$ maximize…

Let an $N\times N\times N$ lattice cube have vertices, and consider subsets of its vertices containing no eight corners of a rectangular box. Erdős's lattice-cube conjecture. The m…

Let $\alpha(k,n)$ denote the minimum number of entries equal to $1$ in an $n\times n$ matrix with entries $0$ and $1$ such that every $k\times k$ minor contains at least one entry…