2021/08/29 by G. Vardanyan, Vardanyan, G. K.
Mathematics · Computer Science · Engineering · #Advanced Differential Equations and Dynamical Systems #Coding theory and cryptography #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2108.12799
An n-correct node set X is called GCn set if the fundamental polynomial of each node is a product of n linear factors. In 1982 Gasca and Maeztu conjectured that for every GCn 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.