Symmetric designs as the solution of an extremal problem in combinatorial set theory
type: Item
instance of: scholarly article
title: Symmetric designs as the solution of an extremal problem in combinatorial set theory
zbMATH Open document ID: 0654.05007
DOI: 10.1016/S0195-6698(88)80043-X
published in: European Journal of Combinatorics
publication date: 1988-01-01T00:00:00Z
review text: A proof is given for the result that \(\nu <(k^2-k+\lambda)/\lambda\) for an equi-replicated, equi-set sized design in \(\nu\) symbols and set size \(k\), where any two sets intersect in at least \(\lambda\) symbols. The equality is attained for a symmetric balanced incomplete block design.
reviewed by: D. Raghavarao
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 4066898
zbMATH Keywords: Johnson scheme
zbMATH Keywords: Bose-Mesner algebra
zbMATH Keywords: adjacency matrix
zbMATH Keywords: Hahn polynomial
zbMATH Keywords: symmetric balanced incomplete block design
author: Robert Calderbank
MaRDI profile type: Publication
cites work: Q4742675
cites work: Q5707657
cites work: Q4055513
cites work: Hahn Polynomials, Discrete Harmonics, andt-Designs
cites work: Finite projective spaces and intersecting hypergraphs
cites work: Maximum degree and fractional matchings in uniform hypergraphs
cites work: Q4180391
full work available at URL: s0195-6698(88)80043-x
OpenAlex ID: W2089254378
description: scientific article; zbMATH DE number 4066898