On the representation of configurations in projective spaces
type: Item
instance of: scholarly article
title: On the representation of configurations in projective spaces
zbMATH Open document ID: 0959.51002
DOI: 10.1016/S0378-3758(99)00124-X
author: David G. Glynn
published in: Journal of Statistical Planning and Inference
publication date: 2001-04-24T00:00:00Z
review text: The author discusses embeddings of point-line configurations into projective spaces over a field. A heuristic condition is found that depends upon an invariant called freedom. The author discusses algorithmic methods that implement embeddings. This is applied to \(k_3\)-configurations, which consist of \(k\) points and \(k\) lines, with 3 points on every line and 3 lines through every point. It is shown that every connected \(k_3\)-configuration can be reduced to a single equation, which can be solved to describe every planar embedding. All higher dimensional embeddings can be obtained by lifting these planar embeddings.
reviewed by: Bart De Bruyn
Mathematics Subject Classification ID: 51A20
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 1471126
zbMATH Keywords: representation
zbMATH Keywords: projective space
zbMATH Keywords: point-line configurations
zbMATH Keywords: embeddings
MaRDI profile type: Publication
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full work available at URL: s0378-3758(99)00124-x
OpenAlex ID: W2054675443
description: scientific article; zbMATH DE number 1471126