保向和反向映射半群的一个新表述
A new formulation of the semigroup of orientation-preserving and orientation-reversing mappings
摘要：
我们刻画了各自的映射半群，保持，或保持或反向定向的有限循环，在他们的行动定向三元组和定向四元组。这就证明了后一个半群与所有保持相应圆上弦的交集的映射的半群重合。
英文摘要：
We characterize 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。
