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This article is cited in 1 scientific paper (total in 1 paper)
Mathematics
On $n$-node lines in $GC_n$ sets
G. K. Vardanyan Yerevan State University, Faculty of Mathematics and Mechanics
Abstract:
An $n$-poised node set $\mathcal {X}$ in the plane is called $GC_n$ set, if the fundamental polynomial of each node is a product of linear factors. A line is called $k$-node line, if it passes through exactly $k$-nodes of $\mathcal {X}$ At most $n+1$ nodes can be collinear in $\mathcal {X}$ set and an $(n+1)$-node line is called maximal line. The well-known conjecture of M. Gasca and J.I. Maeztu states that every $GC_n$ set has a maximal line. Until now the conjecture has been
proved only for the cases $n \le 5.$ In this paper we prove some results concerning $n$-node lines, assuming that the Gasca–Maeztu conjecture is true.
Keywords:
polynomial interpolation, Gasca–Maeztu conjecture, $n$-poised set, $GC_n$ set, maximal line, $n$-node line.
Received: 09.03.2021 Revised: 18.03.2021 Accepted: 31.03.2021
Citation:
G. K. Vardanyan, “On $n$-node lines in $GC_n$ sets”, Proceedings of the YSU, Physical and Mathematical Sciences, 55:1 (2021), 44–55
Linking options:
https://www.mathnet.ru/eng/uzeru831 https://www.mathnet.ru/eng/uzeru/v55/i1/p44
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