Group divisible designs GDD($n,n,n,2;\lambda_1,\lambda_2$)

Atthakorn Sakda
Chulalongkorn University

Chariya Uiyyasathian
Chulalongkorn University

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Minisymposium: COMBINATORICS

Content: A \textit{group divisible design} GDD($g = g_1+g_2+ \cdots + g_s,s,k;\lambda_1,\lambda_2$) is an ordered pair ($G, \mathcal{B}$) where $G$ is a $g$-set of treatments which is partitioned into $s$ sets (called \textit{groups}) of sizes $g_1,g_2,\ldots,g_s$, and $\mathcal{B}$ is a collection of $k$-subsets of $G$ called \textit{blocks} such that each pair of elements from the same group appear together in $\lambda_1$ blocks and each pair of elements from distinct groups appear together in $\lambda_2$ blocks. In this talk, for each tuple of integers $(n,\lambda_1,\lambda_2)$ we give a complete solution for the existence problem of GDD($g = n+n+n+2,4,3;\lambda_1,\lambda_2$).

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