A directed triple system of order $v$ (or, DTS$(v)$) is decomposition of the complete directed graph $\vec{K_v}$ into transitive triples. A $v$-good sequencing of a DTS$(v)$ is a permutation of the points of the design, say $[x_1 \; \cdots \; x_v]$, such that, for every triple $(x,y,z)$ in the design, it is not the case that $x = x_i$, $y = x_j$ and $z = x_k$ with $i < j < k$. We prove that there exists a DTS$(v)$ having a $v$-good sequencing for all positive integers $v \equiv 0,1 \bmod {3}$. Further, for all positive integers $v \equiv 0,1 \bmod {3}$, $v \geq 7$, we prove that there is a DTS$(v)$ that does not have a $v$-good sequencing. We also derive some computational results concerning $v$-good sequencings of all the nonisomorphic DTS$(v)$ for $v \leq 7$.

中文翻译：

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有向三重系统的块规避点排序

阶$v$（或DTS$(v)$）的有向三元系统是将完整的有向图$\vec{K_v}$ 分解为传递三元组。DTS$(v)$ 的 $v$-good 排序是设计点的排列，例如 $[x_1 \; \cdots \; x_v]$，这样，对于设计中的每个三元组 $(x,y,z)$，$x = x_i$、$y = x_j$ 和 $z = x_k$ 且 $i < j < k$。我们证明存在一个 DTS$(v)$ 对所有正整数 $v \equiv 0,1 \bmod {3}$ 具有 $v$-good 排序。此外，对于所有正整数 $v \equiv 0,1 \bmod {3}$, $v \geq 7$，我们证明存在一个 DTS$(v)$ 没有 $v$-good 排序. 我们还推导出了一些关于 $v\leq 7$ 的所有非同构 DTS$(v)$ 的 $v$-good 序列的计算结果。