On the Gasca-Maeztu conjecture for n=6

08/14/2022

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by   Hakop Hakopian, et al.

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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≤ 5. In this paper, we make a step for proving the case n=6.