4 problems

Let $n\in\mathbb{N}$ be a centred hexagonal number, and consider the smallest hexagon containing $n$ disks and the smallest hexagon containing $n-1$ disks. Centred-hexagonal-number…

Let $n>3$ be a triangular number, and consider the smallest triangle containing $n$ disks and the smallest triangle containing $n-1$ disks. Erdős–Oler-type conjecture. The smallest…

Let $n$ unit disks be given, and let $m$ be a positive integer such that … The smallest triangle containing these disks is an equilateral triangle of side length $2(m-1)+2\sqrt{3}$…

Let $(M,\rho)$ be a reversible random planar map. The Martin boundary of $M$ is the boundary describing asymptotic behavior of positive harmonic functions for random walk on $M$. A…