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@article{Carnicer2005GeometricCA, title={Geometric characterization and generalized principal lattices}, author={Jes{\'u}s M. Carnicer and Carmen God{\'e}s}, journal={Journal of Approximation Theory}, year={2005}, volume={143}, pages={2-14} }

- Published in Journal of Approximation Theory 2005
DOI:10.1016/j.jat.2006.02.003

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… CONTINUE READING