Generalized balanced tournament designs

Lamken, E. R.

doi:10.1090/S0002-9947-1990-0978380-6

Generalized balanced tournament designs
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Trans. Amer. Math. Soc. 318 (1990), 473-490 Request permission

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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