A graphical calculus approach to planar st graphs
A graphical calculus approach to planar st graphs
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发表时间：
2016-04
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通讯作者：
Seng Hu;Xuexing Lu;Yu Ye
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作者：
Seng Hu;Xuexing Lu;Yu Ye
平面$st$图是一类特殊的有向平面图，在平面作图、平面上作图、平面偏序集理论等领域中起着重要的作用。本文对平面$st$图进行了一种新的研究，它实质上是张量范畴图演算的一种组合形式。该方法的核心是渐进平面图及其平面序的合成理论，它为计算向上平面图的共轭序提供了一种新的方法。这一工作揭示了图演算与平面图之间的联系，为无圈有向图和偏序集的研究提供了新的思路，更重要的是，为进一步研究向上平面度的亏格理论铺平了道路。
Planar $st$ graphs are special oriented plane graphs that play crucial roles in many areas such as planar drawing, upward planar drawing, planar poset theory, etc. In this paper, we start a new approach to planar $st$ graphs, which is essentially a combinatorial formulation of graphical calculus for tensor categories. The crux of this approach is a composition theory of progressive plane graphs and their planar orders, which provides a new method to calculate the conjugate order of an upward planar $st$ graph. This work reveals the connection between graphical calculus and planar $st$ graphs, which sheds a new light on the study of acyclic directed graphs and posets, and more importantly, paves a way to a higher genus theory of upward planarity.