2 problems

For $w\ge 1$ and integers $1\le k_1\le\cdots\le k_w$, say that two vectors $A,B\in\mathbb{Z}^w$ are $(k_1,\ldots,k_w)$-crossing if there are coordinates $i,j$ such that…

For positive integers $k$ and $w$, let $f(k,w)$ be the maximum size of a subset of $\mathbb{Z}^w$ in which every two vectors are $1$-crossing but no two vectors are $k$-crossing. F…