Planar configurations with simple Lagrange interpolation formulae
Mathematical Methods for Curves and Surfaces
Cubic pencils of lines and bivariate interpolation
Journal of Computational and Applied Mathematics
Configurations of nodes with defects greater than three
Journal of Computational and Applied Mathematics
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The sets of nodes in the plane for which its nth degree Lagrange polynomials can be factored as a product of first degree polynomials satisfy a geometric characterization: for each node there exists a set of @?n lines containing the other nodes. Generalized principal lattices are sets of nodes defined by three families of lines. A generalized principal lattice satisfies the geometric characterization and there exist exactly three lines in the plane containing more nodes than the degree. In this paper, we show a converse, valid for degrees n@?7: if a set of nodes satisfy the geometric characterization and there exist exactly three lines containing n+1 nodes, then it is a generalized principal lattice.