3 problems

Let $n$ and $k$ be integers with $1leq k<n$. For $i,j\in\mathbb{Z}_n$, let … be the circular distance, and let $\sigma(n,k)$ be the largest positive integer $s$ for which there is…

Isostatic conjecture. The density $\rho$ of every such packing satisfies

Let $N$ be the number of equal disks packed in a torus given by a triangular lattice. Suppose that $N$ is not of the form … for integers $a,b$. Triangular-torus density conjecture.…