Ann-poised node setXin the plane is calledGCnset, if the fundamentalpolynomial of each node is a product of linear factors. A line is calledk-nodeline, if it passes through exactlyk-nodes ofX.At mostn+1nodes can becollinear inXand an(n+1)-node line is called maximal line. The well-knownconjecture of M. Gasca and J.I. Maeztu states that everyGCnset has a maximalline. Until now the conjecture has been proved only for the casesn≤5.Inthis paper we prove some results concerningn-node lines, assuming that theGasca–Maeztu conjecture is true.
DOI: 10.46991/PYSU:A/2021.55.1.044 Physical and Mathematical Sciences, 55(1 (254) 44-55
