Radon’s construction and matrix relations generating syzygies

Abstract

AbstractLet $$\varPi _n$$Πn be the set of bivariate polynomials of degree not greater than n. A $$\varPi _n$$Πn-correct set of nodes is a set such that the Lagrange interpolation problem with respect to these nodes has a unique solution. A maximal line of a $$\varPi _n$$Πn-correct set is any line containing exactly $$n+1$$n+1 nodes. Syzygy matrices can be used to find linear factors of the fundamental polynomials and detect maximal lines. We suggest to use matrix relations in order to generate syzygies, identify linear factors of fundamental polynomials and detect maximal lines. We interpret our results in the important case of GC sets trying to shed some light on the Gasca-Maeztu conjecture.