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arXiv · 2208.06784

On the Gasca-Maeztu conjecture for $n=6$

Hakop Hakopian·Gagik Vardanyan·Navasard Vardanyan
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Abstract

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 $n=6.$

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Hakop Hakopian, Gagik Vardanyan, Navasard Vardanyan. 2022-08-14. On the Gasca-Maeztu conjecture for $n=6$. https://arxiv.org/abs/2208.06784

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