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(CC BY-NC 4.0).
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.