论文标题
表面上图上的二元性和互惠性
Dualities and reciprocities on graphs on surfaces
论文作者
论文摘要
我们通过引入边界无环方向和完全可遵循的方向，将平面图上的无环方向和完全循环方向之间的二元性扩展到可定向表面上的偶性。此外，我们还提供了连接局部紧张局势和边界无环方向的互惠定理。此外，我们定义了平衡的流多项式，该流量多项式通过二元性与张力多项式连接，并通过互惠互相进行完全可行的方向。
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.
