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Research Article Open access CC BY 4.0

The Gasca-Maeztu Conjecture for n = 4

Vahagn Vardanyan

Asian Research Journal of Mathematics · pp. 1–7 · Published 20 Feb 2019

10.9734/arjom/2019/v12i230083

Abstract

We consider planar GCn node sets, i.e., n-poised sets whose all n-fundamental polynomials are products of n linear factors. Gasca and Maeztu conjectured in 1982 that every such set possesses a maximal line, i.e., a line passing through n + 1 nodes of the set. Till now the conjecture is confirmed to be true for n ≤ 5. The case n = 5 was proved recently by H. Hakopian, K. Jetter, and G. Zimmermann (Numer. Math. 127 (2014) 685{713). In this paper we bring a short and simple proof of the conjecture for n = 4.

Polynomial interpolation Gasca-Maeztu conjecture fundamental polynomial maximal line n-poised set n-independent set.

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