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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Generalized balanced tournament designs


Author: E. R. Lamken
Journal: Trans. Amer. Math. Soc. 318 (1990), 473-490
MSC: Primary 05B15
DOI: https://doi.org/10.1090/S0002-9947-1990-0978380-6
MathSciNet review: 978380
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Abstract: A generalized balanced tournament design, $ 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. In this paper, we introduce $ GBTD(n,k)s$ and describe connections between these designs and several other types of combinatorial designs. We also show how to use $ GBTDs$ to construct resolvable, near resolvable, doubly resolvable and doubly near resolvable $ BIBDs$.


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DOI: https://doi.org/10.1090/S0002-9947-1990-0978380-6
Article copyright: © Copyright 1990 American Mathematical Society

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