曲面上图的对偶与互反
Dualities and reciprocities on graphs on surfaces
摘要：
通过引入边界无圈定向和全双可走定向，将可平面图上无圈定向和全圈定向的对偶性推广到可定向曲面上图的对偶性.此外，我们提供了一个互易定理连接局部紧张局势和边界无环取向。此外，我们还定义了平衡流多项式，它通过对偶性与张力多项式相联系，并通过互易性与完全双可行走的方向相联系。
英文摘要：
We extend the duality between acyclic orientations and totally cyclic orientations on planar graphs to dualities on graphs on orientable surfaces by introducing boundary acyclic orientations and totally bi-walkable orientations. In addition, we provide a reciprocity theorem connecting local tensions and boundary acyclic orientations. Furthermore, we define the balanced flow polynomial which is connected with tension polynomial by duality and with totally bi-walkable orientations by reciprocity.
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