\(k\)-arcs and dual \(k\)-arcs
type: Item
instance of: scholarly article
title: \(k\)-arcs and dual \(k\)-arcs
zbMATH Open document ID: 0798.51016
DOI: 10.1016/0012-365X(94)90177-5
published in: Discrete Mathematics
publication date: 1994-05-05T00:00:00Z
review text: In \(\text{PG}(n,q)\), a \(k\)-arc is a set of \(k\) points such that \(k\geq n+1\) but not \(n+1\) points belong to a hyperplane. A normal rational curve in \(\text{PG}(n,q)\), \(2\leq n\leq q-2\) is a \(q+1\) arc projectively equivalent to the set of points \(\{(1,t, \cdots, t^ n)\mid t\in \text{GF} (q)^ +\}\) where \(\text{GF}(q)^ +\) denotes \(\text{GF}(q)\cup \{\infty\}\). Some of the main results: Theorem 2.1. A \(k\)-arc in \(\text{PG}(n,q)\), \(k\geq n+4\) and a dual \(k\)- arc \(\widehat{K}\) in \(\text{PG} (k-n-2,q)\) have isomorphic collineation groups. Theorem 3.2. In \(\text{PG}(q-2,q)\), \(q\) even, any point \(p\) which extends a normal rational curve \(K\) to a \(q+2\)-arc belongs to all osculating hyperplanes of \(K\).
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 562680
zbMATH Keywords: \(k\)-arcs
zbMATH Keywords: dual \(k\)-arcs
author: Leo Storme
author: Joseph A. Thas
reviewed by: Theodore G. Ostrom
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 562680