Strongly regular designs and coherent configurations of type \([{32\atop\;3}]\)
type: Item
instance of: scholarly article
title: Strongly regular designs and coherent configurations of type \([{32\atop\;3}]\)
zbMATH Open document ID: 0659.05033
DOI: 10.1016/S0195-6698(88)80072-6
author: D. G. Higman
published in: European Journal of Combinatorics
publication date: 1988-01-01T00:00:00Z
review text: Strongly regular designs arise in the study of coherent configurations. They may, however, be defined in purely design-theoretic terms as follows: A strongly regular design is a finite incidence structure satisfying the following three axioms and their duals: (1) Each block has \(s_ 1\) points. (2) Two distinct blocks intersect in either \(a_ 1\) or \(b_ 1\) points (where \(a_ 1>b_ 1)\), and both cases occur. (3) The number of blocks through a point \(x\) intersecting a given block \(y\) in \(a_ 1\) points is either \(N_ 2\) or \(P_ 2\), depending only on whether x and y are incident or not. As a consequence, both the point and the block graph of an SRD are strongly regular graphs. SRD's are \(1\)-designs in the sense of \textit{A. Neumaier} [``\(t\)-designs'', J. Comb. Theory, Ser. A 28, 226-248 (1980; Zbl 0433.05012)]. They include those partial geometries which are neither 2-designs nor dual 2-designs. In the present paper, the author gives a systematic study of strongly regular designs.
reviewed by: Dieter Jungnickel
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 4077239
zbMATH Keywords: coherent configuration
zbMATH Keywords: Strongly regular designs
zbMATH Keywords: SRD
zbMATH Keywords: partial geometries
MaRDI profile type: Publication
cites work: Q3686719
cites work: On a class of partially balanced incomplete block designs
cites work: Special partially balanced incomplete block designs and associated graphs
cites work: Q3218138
cites work: Inequalities for quasisymmetric designs
cites work: Strongly Regular Graphs Derived from Combinatorial Designs
cites work: Coherent algebras
cites work: Rank 5 association schemes and triality
cites work: Distance-biregular graphs with 2-valent vertices and distance regular line graphs
cites work: \(t{1\over 2}\)-designs
cites work: Q3960709
cites work: Some sporadic geometries related to PG(3,2)
cites work: Q3335798
cites work: The polarities of the partial geometry pg(5,5,2)
full work available at URL: s0195-6698(88)80072-6
OpenAlex ID: W1969582037
description: scientific article; zbMATH DE number 4077239