Polarities in n-uniform projective Hjelmslev planes
type: Item
instance of: scholarly article
title: Polarities in n-uniform projective Hjelmslev planes
zbMATH Open document ID: 0655.51005
DOI: 10.1007/BF00151669
published in: Geometriae Dedicata
publication date: 1988-01-01T00:00:00Z
review text: The definition of an n-uniform projective Hjelmslev plane given in this paper is equivalent with Drake's definition [\textit{D. A. Drake}, J. Comb. Theory 9, 267-288 (1970; Zbl 0204.210)] by \textit{G. Törner} [Mitt. Math. Sem. Giessen 107, 77 S. (1974; Zbl 0287.05022)]. A polarity of an n-uniform projective Hjelmslev plane (P,B,I) is defined as a one-to-one mapping from point-set onto the line-set and from the line-set onto the point-set such that incidence and neighbor relation are preserved. In Geom. Dedicata 24, 51-76 (1987; Zbl 0628.51007) the author has studied polarities in finite 2-uniform projective Hjelmslev planes. The present paper extends the author's results for finite n-uniform projective Hjelmslev planes with \(n\geq 2\). Here, a general formula for the number of absolute points is obtained, polarities in the Pappian n- uniform projective Hjelmslev planes are studied and configurations formed by the absolute points are investigated.
reviewed by: K.Burian
Mathematics Subject Classification ID: 51D20
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 4069691
zbMATH Keywords: polarities
zbMATH Keywords: n-uniform projective Hjelmslev planes
author: Dirk Keppens
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00151669
OpenAlex ID: W2076596267
description: scientific article; zbMATH DE number 4069691