11 problems

Pinned symmetric Laman conjecture. The standard Laman-type conditions for $G$, together with the additional necessary conditions concerning the number of fixed joints and bars, sho…

Extension conjecture. The proofs of this paper should extend to all odd-order cyclic groups.

Let $C_n$ act freely on the vertices, edges, and loops of an infinitesimally rigid $C_n$-symmetric linearly constrained framework in $\mathbb{R}^2$. A symmetric spanning-subframewo…

Consider a planar framework with $\mathcal{C}_{3v}$ symmetry, freedom number $k=0$, and $v_c=0$. If $e_{\sigma}=1$, then there are no symmetry-detectable self-stresses or mechanism…

Let $\|\cdot\|_{\mathcal{P}}$ be a polyhedral norm on $\mathbb{R}^2$ whose unit ball $\mathcal{P}$ is a quadrilateral. Let $G$ be a finite simple graph, let $\Gamma$ be a group, le…

Let $\|\cdot\|_{\mathcal{P}}$ be a polyhedral norm on $\mathbb{R}^2$ whose unit ball $\mathcal{P}$ is a quadrilateral. Let $G$ be a finite simple graph, let…

Let $\mathcal{Y}$ denote the cylinder. Let $S$ be either the group $\mathcal{C}_s$ or the group $\mathcal{C}_i$, and let $(G,p)$ be an $S$-generic framework on $\mathcal{Y}$. The c…

Let $\mathcal{S}$ denote the sphere. For a $S$-symmetric framework, let $S$ be either the group $\mathcal{C}_{mh}$ with $m$ even or the group $\mathcal{S}_{2m}$ with $m$ odd. Let…

Odd-rotation conjecture. The framework $(G,\mathbf{p})$ is infinitesimally rigid if and only if $G$ is 2-rigid.

Symmetric body-hinge transfer conjecture. Given suitable symmetry constraints, the results and conjectures concerning symmetric-generic body-bar frameworks should translate directl…

Symmetric Laman sufficiency conjecture. The Laman conditions, together with the corresponding additional conditions concerning the number of fixed structural components, should be…