Good sequencings for small directed triple systems

A directed triple system of order $v$ (or, DTS$(v)$) is a decomposition of the complete directed graph $\vec{K_v}$ 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...

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Bibliographic Details
Main Authors Kreher, Donald L, Stinson, Douglas R, Veitch, Shannon
Format Journal Article
LanguageEnglish
Published 25.07.2019
Subjects
Mathematics - Combinatorics
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Summary:A directed triple system of order $v$ (or, DTS$(v)$) is a decomposition of the complete directed graph $\vec{K_v}$ 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 $k-i+1 \leq \ell$. In this report we provide a maximum $\ell$-good sequencing for each DTS$(v)$, $v \leq 7$.
DOI:10.48550/arxiv.1907.11144