论文标题
在$ n = 6 $的Gasca-Maeztu猜想上
On the Gasca-Maeztu conjecture for $n=6$
论文作者
论文摘要
二维$ n $ correct套件是一组节点，该节点承认独特的双变量插值，最多最多〜$ n $的多项式。我们对所有基本多项式都是线性因素的产品的属性感兴趣的。 1982年，M.〜Gasca和J.〜I .〜Maeztu猜想，任何此类组都必须包含$ n+1 $ collinear节点。到目前为止，这仅以$ n \ leq 5的确认。$在本文中，我们迈出了一个步骤，以证明情况$ n = 6。
A two-dimensional $n$-correct set is a set of nodes admitting unique bivariate interpolation with polynomials of total degree at most ~$n$. We are interested in correct sets with the property that all fundamental polynomials are products of linear factors. In 1982, M.~Gasca and J.~I.~Maeztu conjectured that any such set necessarily contains $n+1$ collinear nodes. So far, this had only been confirmed for $n\leq 5.$ In this paper, we make a step for proving the case $n=6.$
