论文标题
图形覆盖物和扭曲的操作员
Graph coverings and twisted operators
论文作者
论文摘要
鉴于其基本组的图和表示形式，有一个自然相关的扭曲邻接操作员。本文的主要结果是，这些操作员以覆盖地图的图形方式行事。当该操作员可用于枚举对象或计算分区功能时，这对相应的枚举问题或统计力学模型具有具体的影响。例如，我们表明，如果$ \widetildeγ$是有限连接的覆盖图$γ$的图形图，并带有边缘赋予$ x = \ {x_e \} _ e $，则$γ$的跨越树分区函数将$ \ \ \ \ \ \ \ \ the $ \ \ \ \ \ mathbb = Z}获得了其他几个后果，有些已知，另一些则获得了新的后果。
Given a graph and a representation of its fundamental group, there is a naturally associated twisted adjacency operator. The main result of this article is the fact that these operators behave in a controlled way under graph covering maps. When such an operator can be used to enumerate objects, or compute a partition function, this has concrete implications on the corresponding enumeration problem, or statistical mechanics model. For example, we show that if $\widetildeΓ$ is a finite connected covering graph of a graph $Γ$ endowed with edge-weights $x=\{x_e\}_e$, then the spanning tree partition function of $Γ$ divides the one of $\widetildeΓ$ in the ring $\mathbb{Z}[x]$. Several other consequences are obtained, some known, others new.
