Orbits of arcs in PG\((N,K)\) under projectivities
type: Item
instance of: scholarly article
title: Orbits of arcs in PG\((N,K)\) under projectivities
zbMATH Open document ID: 0751.51001
DOI: 10.1007/BF00147548
author: Carl E. Gordon
published in: Geometriae Dedicata
publication date: 1992-09-27T00:00:00Z
review text: Let \(K\) be a field; let \(k\), \(M\), \(N\) be integers such that \(k=M+N+2\). The author considers equivalence classes of \(k\)-arcs in \(PG(N,K)\), where two \(k\)-arcs are equivalent if one can be carried into the other by a projectivity in \(PG(N,K)\). He considers permutations on a certain set of \(M\) by \(N\) matrices over \(k\) and develops a \(1-1\) correspondence between matrix orbits under this set of permutations and \(k\)-arc orbits under projectivity. From this he obtains the number of \(k\)-arc orbits.
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 57582
zbMATH Keywords: projectivities
zbMATH Keywords: \(k\)-arcs in \(PG(N,K)\)
reviewed by: Theodore G. Ostrom
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00147548
OpenAlex ID: W2061838236
description: scientific article; zbMATH DE number 57582