Generalized Bhaskar Rao designs of block size three
type: Item
instance of: scholarly article
title: Generalized Bhaskar Rao designs of block size three
zbMATH Open document ID: 0572.05021
DOI: 10.1016/0378-3758(85)90042-4
published in: Journal of Statistical Planning and Inference
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://ro.uow.edu.au/infopapers/1016
review text: W is a generalized Bhaskar Rao design with parameters (v,b,r,k,\(\lambda\) ;G) if W has entries from G or 0 - the zero of the group ring - so that if \((a_{i1},...,a_{ib})\) and \((b_{j1},...,B_{jb})\) are distinct rows of W then the scalar product \((WW^+)_{ij}=(a_{i1},...,a_{ib})\cdot (b_{i1},...,b_{jb})\) should give each element of G the same number of times (\(\lambda\) /\(| G|)\). If A is obtained from W by making each non-zero element 1 then A should be the incidence of a BIBD (v,b,r,k,\(\lambda)\). This paper finishes the proof of \textit{C. Lam} and the author [ibid. 10, 83-95 (1984; Zbl 0552.05012)] and the author [ibid. 10, 69-82 (1984; Zbl 0552.05011)] showing that ''The necessary conditions \(\lambda \equiv 0\quad (mod | G|),\) \(\lambda (v-1)\equiv 0\quad (mod 2),\) \(\lambda v(v- 1)\equiv 0\quad (mod 6)\) for \(| G|\) odd, \(\lambda v(v-1)\equiv 0\quad (mod 24)\) for \(| G|\) even, are sufficient for the existence of a generalized Bhaskar Rao design GBRD (v,b,r,3,\(\lambda\) ;G) for the elementary abelian group G, of each order \(| G|\).
Mathematics Subject Classification ID: 05B99
zbMATH DE Number: 3912402
zbMATH Keywords: balanced incomplete block designs
zbMATH Keywords: generalized Bhaskar Rao design
zbMATH Keywords: BIBD
zbMATH Keywords: GBRD
author: Jennifer Seberry
MaRDI profile type: Publication
OpenAlex ID: W2056494552
cites work: Q5592263
cites work: Generalized Bhaskar Rao designs
cites work: Q3949069
cites work: Regular group divisible designs and Bhaskar Rao designs with block size three
description: scientific article; zbMATH DE number 3912402