线性约束框架刚度的一个改进界
An improved bound for the rigidity of linearly constrained frameworks
摘要：
本文考虑了$\mathbb{R}^d$中杆系框架的类属刚度的刻画问题，其中每个顶点被约束在一个给定的仿射子空间中。当$d=2$已由I. Streinu和L. Theran在2010年提出的问题，以及每个顶点被约束在$t$维的仿射子空间中的情况，$d\geq t(t-1)$由Cruickshank，Guler和前两位作者在2019年解决。我们扩展后一个结果表明，无论何时$d\geq 2t$，给定的表征持有。
英文摘要：
We consider the problem of characterising the generic rigidity of bar-joint frameworks in $\mathbb{R}^d$ in which each vertex is constrained to lie in a given affine subspace. The special case when $d=2$ was previously solved by I. Streinu and L. Theran in 2010 and the case when each vertex is constrained to lie in an affine subspace of dimension $t$, and $d\geq t(t-1)$ was solved by Cruickshank, Guler and the first two authors in 2019. We extend the latter result by showing that the given characterisation holds whenever $d\geq 2t$.
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。
