On \(STD_{\frac{k}{3}}[k;3]\)'s
type: Item
instance of: scholarly article
title: On \(STD_{\frac{k}{3}}[k;3]\)'s
zbMATH Open document ID: 1158.05013
author: Kenzi Akiyama
author: Chihiro Suetake
published in: Discrete Mathematics
publication date: 2009-01-28T00:00:00Z
review text: A \textsl{transversal design} TD\(_\lambda[k;u]\) is a set of \(ku\) points \(V\) partitioned into \(k\) classes (or groups) each of size \(u\) and a collection \(\mathcal B\) of \(k\)-subsets of \(V\) called blocks for which (1) no pair of points from the same class is a subset of a block and (2) every pair of points from different classes is a subset of exactly \(\lambda\) of the blocks. It is a \textsl{symmetric transversal design} STD\(_\lambda[k;u]\) if, in addition, the dual structure forms a TD\(_\lambda[k;u]\), and hence \(k = \lambda u\). In this paper, the existence of STD\(_{k/3}[k;3]\)s that admit an automorphism acting regularly on the point groups and on the block groups are studied. A computer search is undertaken for \(k \leq 21\) and properties of the designs are reported.
reviewed by: Charles J. Colbourn
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 51E14
zbMATH DE Number: 5499784
zbMATH Keywords: symmetric transversal design
zbMATH Keywords: automorphism group
zbMATH Keywords: generalized Hadamard matrix
MaRDI profile type: Publication
full work available at URL: j.disc.2007.12.034
OpenAlex ID: W1989681138
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DOI: 10.1016/J.DISC.2007.12.034
description: scientific article; zbMATH DE number 5499784