Existence results for generalized balanced tournament designs with block size 3
type: Item
instance of: scholarly article
title: Existence results for generalized balanced tournament designs with block size 3
zbMATH Open document ID: 0791.05010
DOI: 10.1007/BF01389354
author: Esther R. Lamken
published in: Designs, Codes and Cryptography
publication date: 1993-05-16T00:00:00Z
review text: A generalized balanced tournament design, \(\text{GBTD} (n,k)\) defined on a \(kn\)-set \(V\), is an arrangement of the blocks of a \((kn,k,k-1)\)-BIBD defined on \(V\) into an \(n \times (kn-1)\) array such that (1) every element of \(V\) is contained in precisely one cell of each column, and (2) every element of \(V\) is contained in at most \(k\) cells of each row. By utilizing direct and recursive constructions, the author completely determines the spectrum of \(\text{GBTD} (n,3)\). It is also proved that all positive integers \(n \geq 4\) belong to the spectrum of a factored \(\text{GBTD} (n,3)\), with one possible exception when \(n=23\).
reviewed by: M.Oravas
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 167549
zbMATH Keywords: generalized balanced tournament design
zbMATH Keywords: spectrum
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01389354
OpenAlex ID: W2022562302
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description: scientific article; zbMATH DE number 167549