论文标题
多边形作为一个可集成系统的群集
Polygon recutting as a cluster integrable system
论文作者
论文摘要
重新爆发是通过沿对角线切除多边形以去除三角形的平面多边形的操作，然后将三角形沿着相同的对角线重新连接，但具有相反的方向。沿不同对角线的重新介绍产生了仿射对称组对多边形空间的作用。我们表明，此操作是由集群变换给出的，并且是完全可以集成的。整合性证明是基于对重构Quaternionic多项式重构的解释。
Recutting is an operation on planar polygons defined by cutting a polygon along a diagonal to remove a triangle, and then reattaching the triangle along the same diagonal but with opposite orientation. Recuttings along different diagonals generate an action of the affine symmetric group on the space of polygons. We show that this action is given by cluster transformations and is completely integrable. The integrability proof is based on interpretation of recutting as refactorization of quaternionic polynomials.
