论文标题
通用对称性的无限刚性：翻译和旋转
Generic symmetry-forced infinitesimal rigidity: translations and rotations
论文作者
论文摘要
我们表征了平面中对称框架的组合类型，当对称组由旋转和翻译组成时，这些框架是最小的一般对称性无限性刚性的。在此过程中，我们使用热带几何形状来展示如何使用将矩阵与子模函数相关联的Edmond的构造，以描述两个线性空间的Hadamard乘积的代数矩阵，以每个线性空间的矩形。这导致了Laman定理的新的，简短的证明，以及Jord {Á} N，Kaszanitzky和Tanigawa的定理，以及Malestein和Malestein和Theran在对称组仅包含轮换时在平面上在平面上在平面上表征最低的对称性刚性图。
We characterize the combinatorial types of symmetric frameworks in the plane that are minimally generically symmetry-forced infinitesimally rigid when the symmetry group consists of rotations and translations. Along the way, we use tropical geometry to show how a construction of Edmonds that associates a matroid to a submodular function can be used to give a description of the algebraic matroid of a Hadamard product of two linear spaces in terms of the matroids of each linear space. This leads to new, short, proofs of Laman's theorem, and a theorem of Jord{á}n, Kaszanitzky, and Tanigawa, and Malestein and Theran characterizing the minimally generically symmetry-forced rigid graphs in the plane when the symmetry group contains only rotations.
