4 problems

For positive integers $t$ and $r$, consider optimal $(t,r)$ broadcasts on the infinite grid and their densities. Blessing et al.'s conjecture. The optimal $(t,r)$ and $(t+1,r+2)$ b…

Let $t$ and $r$ be positive integers, and let $\delta_{t,r}(\mathbb{Z}^2)$ denote the minimum density of a $(t,r)$-broadcasting set in the infinite square grid. Asymptotic sharpnes…

Let $t,r$ be positive integers, and let $\delta_{t,r}(\mathbb{Z}^2)$ denote the minimum density of a $(t,r)$-broadcasting set in the infinite square grid. The preceding bounds comp…

Let $G_\infty$ be the infinite grid, and let $\delta_{t,r}(G_\infty)$ denote the minimum density of a $(t,r)$ broadcast. Revised broadcast-density conjecture. For all $t>2$, … This…