The isomorphism of the Cohen, Haemers-van Lint and de Clerk-Dye-Thas partial geometries
type: Item
instance of: scholarly article
title: The isomorphism of the Cohen, Haemers-van Lint and de Clerk-Dye-Thas partial geometries
zbMATH Open document ID: 0541.51017
DOI: 10.1016/0012-365X(84)90122-5
author: Vladimir D. Tonchev
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: A. M. Cohen constructed a partial geometry pg(8,9,4) using group theory. Independently, using coding theory, W. Haemers and J. H. van Lint obtained a partial geomery with the same parameters. Later on, F. De Clerk, R.H. Dye and the reviewer described an infinite class of partial geometries \(pg(2^{2n-1},2^{2n-1}+1,2^{2n-2})\). So for \(n=2\) there arises again a pg(8,9,4). In ''Strongly regular graphs defined by spreads ''[Israel J. Math. 41, 298-312 (1982; Zbl 0524.05020)], \textit{W. M. Kantor} proved that the pg(8,9,4)'s of Haemers-van Lint and De Clerck-Dye-Thas are isomorphic. Here Tonchev proves the isomorphism between the pg(8,9,4)'s of Cohen and Haemers-van Lint.
Mathematics Subject Classification ID: 51E30
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 3859874
zbMATH Keywords: partial geometries
zbMATH Keywords: isomorphism
MaRDI profile type: Publication
cites work: Strongly regular graphs, partial geometries and partially balanced designs
cites work: A new partial geometry with parameters \((s,t,\alpha)=(7,8,4)\)
cites work: An infinite class of partial geometries associated with the hyperbolic quadric in \(\mathrm{PG}(4n-1,2)\)
cites work: A Partial Geometry pg(9, 8, 4)
cites work: Strongly regular graphs defined by spreads
full work available at URL: 0012-365x(84)90122-5
OpenAlex ID: W2095240039
description: scientific article; zbMATH DE number 3859874