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...

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Bibliographic Details
Published inarXiv.org
Main Authors Kreher, Donald L, Stinson, Douglas R, Veitch, Shannon
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.11.2019
Subjects
Graph theory
Permutations
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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\((v)\), \(v \leq 7\).
ISSN:2331-8422