Mendelsohn三元系的避块点序列
Block-avoiding point sequencings of Mendelsohn triple systems
摘要：
$v$阶的门德尔松三元系（或MTS $(v)$）中的点的循环排序称为排序。如果MTS $(v)$中不存在三重$(x,y,z)$，则测序$D$是$\ell$ -良好的，使得（1）三个点$x,y,$和$z$在$D$中以该顺序（循环地）出现;并且（2）$\{x,y,z\}$是$D$的$\ell$循环连续点的子集。在本文中，我们证明了一些上界$\ell$ MTS $(v)$有$\ell$ -良好的排序，我们证明了任何MTS $(v)$与$v \geq 7$有$3$ -良好的排序。我们还确定了每个MTS $(v)$与$v \leq 10$的最佳序列。
英文摘要：
A cyclic ordering of the points in a Mendelsohn triple system of order $v$ (or MTS$(v)$) is called a sequencing. A sequencing $D$ is $\ell$-good if there does not exist a triple $(x,y,z)$ in the MTS$(v)$ such that (1) the three points $x,y,$ and $z$ occur (cyclically) in that order in $D$; and (2) $\{x,y,z\}$ is a subset of $\ell$ cyclically consecutive points of $D$. In this paper, we prove some upper bounds on $\ell$ for MTS$(v)$ having $\ell$-good sequencings and we prove that any MTS$(v)$ with $v \geq 7$ has a $3$-good sequencing. We also determine the optimal sequencings of every MTS$(v)$ with $v \leq 10$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
