2n+1个平面向量的平衡配置
Balanced configurations of 2n+1 plane vectors
摘要：
平面配置{v_1，...，{ \mathbb R}^2中向量的v_m}称为平衡的，如果对于任何下标i，j \neq i的det（v_i，v_j）的集合关于原点对称。如果每对向量都是线性无关的，则称平面构形是均匀的。E. Cattani和A. Dickenstein证明了任何一致平衡组态都是GL_2（{ \mathbb R}）-等价于正则（2n+1）-边形。本文证明了这一猜想。
英文摘要：
A plane configuration {v_1,...,v_m} of vectors in {\mathbb R}^2 is said to be balanced if for any index i, the set of the det(v_i,v_j) for j\neq i is symmetric around the origin. A plane configuration is said to be uniform if every pair of vectors is linearly independent. E. Cattani and A. Dickenstein conjectured that any uniform balanced configuration is GL_2({\mathbb R})-equivalent to a regular (2n+1)-gon. In this note, we prove this conjecture.
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。
