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arXiv · 1909.06475

Good sequencings for small Mendelsohn triple systems

Donald L. Kreher·Douglas R. Stinson·Shannon Veitch
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Abstract

A Mendelsohn triple system of order $v$ (or MTS$(v)$) is a decomposition of the complete graph into directed 3-cyles. We denote the directed 3-cycle with edges $(x,y)$, $(y,z)$ and $(z,x)$ by $(x,y,z)$, $(y,z,x)$ or $(z,x,y)$. An $\ell$-good sequencing of a MTS$(v)$ 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 $k-i+1 \leq \ell$; or with $j < k < i$ and $i-j+1 \leq \ell$; or with $k < i < j$ and $j-k+1 \leq \ell$.

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Donald L. Kreher, Douglas R. Stinson, Shannon Veitch. 2019-09-13. Good sequencings for small Mendelsohn triple systems. https://arxiv.org/abs/1909.06475

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