2 problems

Let a $GC_n$ set be an $n$-correct set $\mathcal{X}$ in which the fundamental polynomial of every node is a product of $n$ linear factors. Gasca–Maeztu conjecture. Any $GC_n$ set c…

Conjecture concerning $GC_n$ sets. There is an integer $s$ with $2k-n-1\leq s\leq k$ such that