2 problems

Let $X$ be a $GC_{d,n}$ set in ${\mathbb R}^d$, and call a hyperplane maximal when it contains ${d-1+n\choose n}$ points of $X$. de Boor's multiple-maximal-hyperplane conjecture. E…

Let $X$ be a $GC_{d,n}$ set in ${\mathbb R}^d$: it has ${n+d\choose d}$ points, and for every $p\in X$ there is a product of $n$ linear forms that equals $1$ at $p$ and $0$ at ever…