论文标题
第二级转换半群作为图形上的连续图：基础和结构
Degree 2 Transformation Semigroups as Continuous Maps on Graphs: Foundations and Structure
论文作者
论文摘要
我们开发了具有2度的转换分离群的理论，即通过部分函数对有限集进行起作用，以使点的反相反图像最多具有两个元素。我们表明，这种作用的纤维图在半群论和图理论之间有着深厚的联系。众所周知，2度动作的Krohn-rhodes复杂性最多是2。我们表明，图上的连续地图的单体是适当的0简单半群的翻译船体。我们展示了如何将小组映射半群视为其正确字母映射图像的常规封面，并将其与它们的纤维图相关联。
We develop the theory of transformation semigroups that have degree 2, that is, act by partial functions on a finite set such that the inverse image of points have at most two elements. We show that the graph of fibers of such an action gives a deep connection between semigroup theory and graph theory. It is known that the Krohn-Rhodes complexity of a degree 2 action is at most 2. We show that the monoid of continuous maps on a graph is the translational hull of an appropriate 0-simple semigroup. We show how group mapping semigroups can be considered as regular covers of their right letter mapping image and relate this to their graph of fibers.
