Regular partitions of (weak) finite generalized polygons
type: Item
instance of: scholarly article
title: Regular partitions of (weak) finite generalized polygons
zbMATH Open document ID: 1193.51007
author: A. De Wispelaere
author: Hendrik Van Maldeghem
published in: Designs, Codes and Cryptography
publication date: 2009-03-31T00:00:00Z
review text: The authors define a regular \(m\)-partition of a distance regular graph \(\Gamma\) as a partition of the vertex set of \(\Gamma\) into \(m\) classes \(\mathcal P_i\), \(i= 1,\ldots m\), having the property that for any \(x \in \mathcal P_i\) the number of points, \(d_{ij}\), in \(\mathcal P_j\) adjacent to \(x\) depends only on \(i\), i.e., is independent of \(x\). They show that the eigenvalues of the matrix \((d_{ij})\) are strongly linked to those of the adjacency matrix of \(\Gamma\). They exploit this relationship to gain structural information on various substructures of finite generalized polygons. They are able to give unifying, alternative, and more elegant proofs of several results in the literature.
Mathematics Subject Classification ID: 51E12
zbMATH DE Number: 5536719
zbMATH Keywords: generalized polygon
zbMATH Keywords: distance regular graph
zbMATH Keywords: partition
reviewed by: Alberto Luis Delgado
MaRDI profile type: Publication
full work available at URL: s10623-007-9062-9
OpenAlex ID: W2115958923
cites work: Tight sets and \(m\)-ovoids of finite polar spaces
cites work: Q4770409
cites work: On a characterization of the finite twisted triality hexagons using one classical ideal split Cayley subhexagon
cites work: Q4276283
cites work: A distance-2-spread of the generalized hexagon H(3)
cites work: Codes from generalized hexagons
cites work: Some new two-character sets in PG\((5,q^2)\) and a distance-2 ovoid in the generalized hexagon \(H(4)\)
cites work: The nonexistence of certain generalized polygons
cites work: Q3866127
cites work: On the order of a generalized hexagon admitting an ovoid or spread
cites work: Distance-\(j\) ovoids and related structures in generalized polygons
cites work: Q4078050
cites work: A restriction on the parameters of a subhexagon
cites work: Sur la trialité et certains groupes qui s'en déduisent
cites work: Q4217275
DOI: 10.1007/S10623-007-9062-9
description: scientific article; zbMATH DE number 5536719