Geometric characterization and generalized principal lattices

@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}
}
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
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