SIAM Journal on Discrete Mathematics, Volume 35, Issue 2, Page 928-933, January 2021.
We consider the problem of characterizing 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 Streinu and Theran [Discrete Comput. Geom., 44 (2020), pp. 812--837] 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 et al. [Int. Math. Res. Not. IMRN, 12 (2020), pp. 3824--3840]. We extend the latter result by showing that the given characterization holds whenever $d\geq 2t$.

中文翻译：

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线性约束框架刚性的改进边界

SIAM杂志上离散数学，35卷，第2期，页928-933，2021年一月
，我们认为表征$ \ mathbb {R} ^ d $，其中每个顶点受到限制酒吧的联合框架的通用刚性的问题位于给定的仿射子空间中。$d=2$ 的特殊情况先前已由 Streinu 和 Theran [Discrete Comput. Geom., 44 (2020), pp. 812--837] 以及每个顶点被约束在维度为 $t$ 的仿射子空间中的情况，并且 $d\geq t(t-1)$ 由下式求解克鲁克香克等人。[国际。数学。水库 不是。IMRN，12 (2020)，第 3824--3840 页]。我们通过显示给定的特征在 $d\geq 2t$ 时成立来扩展后一个结果。