标题： 周期离散Darboux变换 显示英文标题

标题： Periodic discrete Darboux transforms

摘要： 我们将离散极化曲线的Darboux变换表示为四元数形式中的离散连接的平行截面。 这立即导致了变换的单值性线性化。 我们还考虑了离散自行车对应情况下的可积约化。 将我们的方法应用于离散圆的情况，我们得到了所有（闭合）Darboux变换和（闭合）自行车对应关系的显式离散参数化。 显示英文摘要

摘要： We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider the integrable reduction to the case of discrete bicycle correspondence. Applying our method to the case of discrete circles, we obtain closed-form discrete parametrisations of all (closed) Darboux transforms and (closed) bicycle correspondences.