Flag algebras of symmetric design
type: Item
instance of: scholarly article
title: Flag algebras of symmetric design
zbMATH Open document ID: 0684.05007
DOI: 10.1016/0097-3165(88)90007-6
author: Ken W. Smith
published in: Journal of Combinatorial Theory. Series A
publication date: 1988-01-01T00:00:00Z
review text: If a symmetric design is either the point-hyperplane design of a projective space or the complement of a projective space over a field of order two then the algebra on the flags of the design has a natural extension to a seven-dimensional algebra of an association scheme. The purpose of this paper is to show that under certain additive conditions the converse is true, that is, if the flag algebra has an extension to seven-dimensional algebra of an association scheme then it is one of the designs mentioned above. The conditions are either \(\lambda\) divides k-1 or \(k=22\). The technical proofs use representation theory and counting argument to establish basic equations which imply the results.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 4120179
zbMATH Keywords: symmetric design
zbMATH Keywords: association scheme
zbMATH Keywords: flag algebra
reviewed by: Neal Brand
MaRDI profile type: Publication
full work available at URL: 0097-3165(88)90007-6
OpenAlex ID: W2034671645
cites work: Q3218140
cites work: Near-regularity conditions for designs
cites work: Q3863891
cites work: Hecke algebras and characters of parabolic type of finite groups with (B, N)-pairs
cites work: Q5545191
cites work: Some characterizations of finite projective spaces
cites work: Q5592263
cites work: Coherent configurations. I: Ordinary representation theory
cites work: On the Line Graph of a Symmetric Balanced Incomplete Block Design
cites work: On the theorem of Feit-Higman
cites work: Q3967545
cites work: Tactical configurations and their generic ring
cites work: Q4146667
cites work: Some remarks on representation theory in finite geometry
cites work: Q3333642
cites work: Q3918647
description: scientific article; zbMATH DE number 4120179