6 problems

For each integer $N\geq 2$, let $\epsilon(N)$ be a positive quantity with … as $N$ tends to infinity. Let $M$ be the Markov constant of a packing of $N$ equal disks in a square tor…

Let $N\geq 6$ and consider a rigid packing of $N$ equal disks in a square torus. Assume that its packing graph consists of two linear geodesics, and let $M$ be its Markov constant.…

Square-torus Markov-bound conjecture. Every such packing satisfies $M\leq 6.25$. Equivalently,

Let $N$ equal disks be packed in a square torus. A packing is said to correspond to a convergent of $1/\sqrt{3}$ or $2-\sqrt{3}$ when it is one of the Type I or Type II packings, r…

Let $M(N)$ be the Markov constant of a packing of $N$ disks in a square torus, and consider the two packing sequences constructed in the paper, associated with continued-fraction a…

Let $N$ be the number of equal disks in a square torus, let $\delta(N)$ denote the packing density, and let $\pi/\sqrt{12}$ be the density of the planar hexagonal packing. Square-t…