Geometric characterization and generalized principal lattices

[摘要] 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. (C) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-11-01

[效力级别]  Proceedings Paper