Combinatorial construction of some near polygons
type: Item
instance of: scholarly article
title: Combinatorial construction of some near polygons
zbMATH Open document ID: 0877.51004
author: B. N. Cooperstein
author: E. E. Shult
published in: Journal of Combinatorial Theory. Series A
publication date: 1997-12-14T00:00:00Z
review text: A near \(2n\)-gon is a linear incidence system \((P,L)\) satisfying: (i) every line contains at least two points, (ii) the point graph of \((P,L)\) is connected with diameter \(n\), (iii) for each point line pair \((p,l)\), there is a unique point \(q\) on \(l\) nearest \(p\). Note that near 4-gon is the same thing as a generalized quadrangle. The authors give a recipe which has one ingredient, a rank two incidence geometry with three points on a line and produces a geometry of the same type. The recipe is applied recursively, starting with the geometry consisting of one point and no lines, to obtain the family of dual polar spaces of type \(Sp(2n,2)\). Applying the construction to the Hamming near \(2n\)-gon on \(3^n\) points, the authors obtain some new near \(2n+2\)-gons.
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51A50
zbMATH DE Number: 1016775
zbMATH Keywords: near polygons
zbMATH Keywords: polar space
zbMATH Keywords: generalized quadrangle
reviewed by: Alexandre A. Makhnev
MaRDI profile type: Publication
full work available at URL: jcta.1996.2768
OpenAlex ID: W2011693741
cites work: Q4763522
cites work: Dual polar spaces
cites work: Near \(n\)-gons and line systems
cites work: Sur la trialité et certains groupes qui s'en déduisent
DOI: 10.1006/JCTA.1996.2768
description: scientific article; zbMATH DE number 1016775