5 problems

Perturbation conjecture. For every $\epsilon>0$, there is a set $S'=\{p'_1,p'_2,\ldots,p'_n\}$ in bijective correspondence with $S$ such that each corresponding pair satisfies…

Let $G=(V,E)$ be a graph, let $u,v e in V$ be distinct vertices, and let $X$ be a normed plane. The notions of $uv$-independence and $uv$-sparsity are defined for $G$ in $X$. **The…

Let $X$ be an analytic normed plane, and let $(G,p)$ be a completely regular bar-joint framework, meaning a framework satisfying the paper's notion of complete regularity. A graph…

Let $\mathcal{P}$ be the normed plane under consideration, with unit ball determined by its norm, and let $\lambda_k^1,\lambda_k^2$ denote the two eigenvalue sequences associated w…

Let $K=\{p_1,p_2,\dots,p_n\}$ be a finite set in a normed plane $\mathbb{M}^2$, and let $\lambda\geq\lambda_K$. The ball intersection $\operatorname{bi}(K,\lambda)$ and the ball hu…