ON A CONJECTURE IN BIVARIATE INTERPOLATION

Denote the space of all bivariate polynomials of total degree n≤n by Πn. We are interested in n-poised sets of nodes with the property that the fundamental polynomial of each node is a product of linear factors. In 1981 M. Gasca and J. I.Maeztu conjectured that every such set contains necessarily n+1 collinear nodes. Up to now this had been confirmed for degrees n≤5. Here we bring a simple and short proof of the conjecture for n=4.