Good sequencings for small directed triple systems

Abstract

A directed triple system of order $v$ (or, DTS$(v)$) is a decomposition of the complete directed graph $\overrightarrow{K_v}$ into transitive triples. An $\ell$-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 $i<j<k$ and $k-i+1\le \ell$. In this report we provide a maximum $\ell$-good sequencing for each DTS$(v)$, $v\le 7$.

305 pages