Characterization of some subgraphs of point-collinearity graphs of building geometries
type: Item
instance of: scholarly article
title: Characterization of some subgraphs of point-collinearity graphs of building geometries
zbMATH Open document ID: 1117.51016
author: Anna Kasikova
published in: European Journal of Combinatorics
publication date: 2007-05-18T00:00:00Z
review text: The author gives a beautiful characterization of the shadows of apartments of residues in the point-line truncations of \(J\)-Grassmannians of buildings. In fact, these are characterized by two conditions on a given connected induced subgraph of the point graph of the point-line truncation (a local one and one involving circuits and planes of the \(J\)-Grassmannian); roughly the former controls the thickness (or rather the thinness) and the latter controls the diameter and girth of the rank 2 residues of the subgraph. A number of other results is presented, such as the theorem that the shadow of any residue in the point-line truncation of a J-Grassmannian is a convex subspace. The usefulness of the main theorem is illustrated with a number of examples. The reviewer likes to stress that the results proved in this paper hold for any \(J\) (of course, \(J\) must meet every connected component of the diagram). As such, this paper is a marvellous contribution to the theory of building Grassmannians.
Mathematics Subject Classification ID: 51E24
zbMATH DE Number: 5154718
zbMATH Keywords: Grassmannians
zbMATH Keywords: buildings
zbMATH Keywords: apartments
zbMATH Keywords: shadow spaces
zbMATH Keywords: point-line spaces
reviewed by: Hendrik Van Maldeghem
MaRDI profile type: Publication
full work available at URL: j.ejc.2006.05.020
OpenAlex ID: W2104345372
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DOI: 10.1016/J.EJC.2006.05.020
description: scientific article; zbMATH DE number 5154718