Bitranslations and symmetric nets
type: Item
instance of: scholarly article
title: Bitranslations and symmetric nets
zbMATH Open document ID: 1295.05067
DOI: 10.1155/2010/502989
author: A. N. Al-Kenani
published in: International Journal of Combinatorics
publication date: 2010-11-17T00:00:00Z
review text: Summary: It is known that every class-regular symmetric \((\mu ,m)\)-net is tactical. Also it is known that all \((\mu ,m)\)-nets with \(m=2\) or \(\mu =1\) are tactical. In the work of \textit{A. N. Al-Kenani} and \textit{V. C. Mavron} [J. Lond. Math. Soc., II. Ser. 67, No. 2, 273--288 (2003; Zbl 1042.05020)], it is proved that every symmetric net with \(m=3\) is tactical if and only if it is class regular. In this paper, we construct a \((2,4)\)-net and show that it is class regular and therefore tactical. New necessary and sufficient conditions are given for a symmetric net to admit a nonidentity bitranslation.
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 51E14
zbMATH DE Number: 5816743
zbMATH Keywords: tactical nets
Wikidata QID: Q58651215
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2010/502989
OpenAlex ID: W2033119703
cites work: On difference matrices, resolvable transversal designs and generalized Hadamard matrices
cites work: On symmetric nets and generalized Hadamard matrices from affine designs
cites work: NON-TACTICAL SYMMETRIC NETS
description: scientific article; zbMATH DE number 5816743