Rank 3 incidence structures admitting dual-linear, linear diagram
type: Item
instance of: scholarly article
title: Rank 3 incidence structures admitting dual-linear, linear diagram
zbMATH Open document ID: 0572.51010
DOI: 10.1016/0097-3165(85)90075-5
author: Alan P. Sprague
published in: Journal of Combinatorial Theory. Series A
publication date: 1985-01-01T00:00:00Z
review text: The following result is proved: Let \(\Gamma\) be a finite rank 3 Buekenhout incidence structure admitting diagram \(\circ\overset{^{L^*}}\diagrbar\circ\overset{^L}\diagrbar\circ\). Then for some generalized projective geometry \(\pi\) and some integer \(i\), \(\Gamma\) is isomorphic to the rank 3 Buekenhout incidence structure having all \((i-2)\)-, \((i-1)\)-, and \(i\)-dimensional subspaces of \(\pi\) as varieties, and comparability as the incidence relation. An analogous result is given for a \(\Gamma\) admitting diagram \(\circ\overset{^{c^*}}\diagrbar\circ\overset{^c}\diagrbar\circ\) for some set X.
Mathematics Subject Classification ID: 51E30
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 3913133
zbMATH Keywords: Buekenhout incidence structure
zbMATH Keywords: generalized projective geometry
reviewed by: Grozio Stanilov
MaRDI profile type: Publication
full work available at URL: 0097-3165(85)90075-5
OpenAlex ID: W1980204495
cites work: Diagrams for geometries and groups
cites work: Pasch's axiom and projective spaces
description: scientific article; zbMATH DE number 3913133