保向与反向映射的一种新描述
Orientation-preserving and orientation-reversing mappings: a new description
摘要：
我们分别讨论了保持、保持或反转有限圈定向的映射半群，它们在定向三元组和定向四元组上的作用。这导致了一个证明，后者半群符合半群的所有映射，保持交叉的弦上相应的圆。
英文摘要：
We characterise the respective semigroups of mappings that preserve, or that preserve or reverse orientation of a finite cycle, in terms of their actions on oriented triples and oriented quadruples. This leads to a proof that the latter semigroup coincides with the semigroup of all mappings that preserve intersections of chords on the corresponding circle.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
