3 problems

Contact-number equality conjecture.

For $n\geq 6$, let $c(n,3)$ be the maximum number of contacts among packings of $n$ unit spheres in $\mathbb{E}^{3}$, and call a contact graph minimally rigid when it has the rigid…

Let $\mathbf{c}_i+\mathbf{B}\in {\cal P}$ be tangent to $\mathbf{c}_j+\mathbf{B}\in {\cal P}$ for all $j\in T_i$, where $T_i\subset\{1,2,\dots,n\}$ is the set of indices satisfying…