Strongly regular designs of the second kind
type: Item
instance of: scholarly article
title: Strongly regular designs of the second kind
zbMATH Open document ID: 0832.05101
DOI: 10.1016/0195-6698(95)90003-9
author: D. G. Higman
published in: European Journal of Combinatorics
publication date: 1996-02-20T00:00:00Z
review text: The author introduces a new type of combinatorial design, called a strongly regular design of the second kind, satisfying a rather involved set of axioms. The motivation for this is a connection to the theory of coherent configurations having two fibers of rank 2 or 3; there are 4 types of such configurations, three of which are equivalent to symmetric designs, quasi-symmetric designs and strongly regular designs (of the first kind). In the paper under review, the author shows that the new class of designs is equivalent to coherent configurations of type \(\left[\begin{smallmatrix} 3\\ \phantom 3\end{smallmatrix} \begin{smallmatrix} 3\\ 3\end{smallmatrix}\right]\). He also discusses the known examples (one of them being provided by the lines and colines of \(\text{PG}(m, q)\) for \(m\geq 4\)), parametric restrictions and polarities.
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 798913
zbMATH Keywords: strongly regular design of the second kind
zbMATH Keywords: coherent configurations
zbMATH Keywords: symmetric designs
reviewed by: Dieter Jungnickel
MaRDI profile type: Publication
full work available at URL: 0195-6698(95)90003-9
OpenAlex ID: W2012888001
cites work: Q3333220
cites work: Q3684278
cites work: Coherent algebras
cites work: Strongly regular designs and coherent configurations of type \([{32\atop\;3}]\)
cites work: On the simple group of D.G. Higman and C.C. Sims
description: scientific article; zbMATH DE number 798913