高阶树由多面体图产生的有限高阶平面树。与一棵树的区别

David Pask
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摘要

我们引入了一个新的高阶图族,其构造受到了兰姆贝克(Lambek)和约翰斯通(Johnstone)用于单类和类嵌入结果的图形技术的启发。我们证明了它们是 2 ~ k ~ 4$ 的平面 $k$ 树。我们还举例说明了高阶树与$1$树的区别,因为高阶树具有$1$树不可能具有的性质。最后,我们收集了更多不属于我们家族的高阶平面树的例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Higher-rank trees: Finite higher-rank planar trees arising from polyhedral graphs. Differences from one-trees
We introduce a new family of higher-rank graphs, whose construction was inspired by the graphical techniques of Lambek \cite{Lambek} and Johnstone \cite{Johnstone} used for monoid and category emedding results. We show that they are planar $k$-trees for $2 \le k \le 4$. We also show that higher-rank trees differ from $1$-trees by giving examples of higher-rank trees having properties which are impossible for $1$-trees. Finally, we collect more examples of higher-rank planar trees which are not in our family.
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