On a conjecture in bivariate interpolation (Երկչափ միջարկման մի վարկածի վերաբերյալ)

Համառոտագիր

Denote the space of all bivariate polynomials of total degree ≤ 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.