A new proof of the Gasca-Maeztu conjecture for n = 5

08/29/2021

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by   G. K. Vardanyan, et al.

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An n-correct node set 𝒳 is called GC_n set if the fundamental polynomial of each node is a product of n linear factors. In 1982 Gasca and Maeztu conjectured that for every GC_n set there is a line passing through n+1 of its nodes.So far, this conjecture has been confirmed only for n≤ 5. The case n = 4, was first proved by J. R. Bush in 1990. Several other proofs have been published since then. For the case n=5 there is only one proof: by H. Hakopian, K. Jetter and G. Zimmermann (Numer Math 127,685-713, 2014). Here we present a second, much shorter and easier proof.