More configurations on elliptic curves
type: Item
instance of: scholarly article
title: More configurations on elliptic curves
zbMATH Open document ID: 1546.51001
author: Marco Bramato
author: Lorenz Halbeisen
author: Norbert Hungerbühler
published in: Innovations in Incidence Geometry
publication date: 2024-07-30T00:00:00Z
review text: A \((p_{\lambda}, l_{\pi})\) configuration is a set of \(p\) points and \(l\) lines in a projective plane such that each point is incident with \(\lambda\) lines and each line is incident with \(\pi\) points.\N\NLet \(r\ge s\ge1\) be integers. The authors construct \((3r_{s},sr_{3})\) configurations, where the points are on an elliptic curve. These configurations have a mirror symmetry and if \(3\) divides \(r\) also a rotational symmetry of order three. Moreover, they have the property that the points can be moved along the curve in such a way that incidences are preserved.\N\NIt is an open question whether the points of any such configuration can be placed on an elliptic curve.
reviewed by: Hubert Kiechle
Mathematics Subject Classification ID: 51A20
Mathematics Subject Classification ID: 51A05
zbMATH DE Number: 7889334
zbMATH Keywords: configurations
zbMATH Keywords: elliptic curves
MaRDI profile type: Publication
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DOI: 10.2140/IIG.2024.21.45
description: scientific article; zbMATH DE number 7889334