3 problems

Let $n\in\mathbb{N}$ be even, and let $(B,W)$ be an $(a,b)$-plaid on the torus $\mathbb{T}_n$ for which $\min\{|B|,|W|\}$ is maximum. Even-torus conjecture. Then … The conjecture f…

Let $\xi(n)$ denote the toroidal covering parameter, and let $n$ range over positive integers. Asymptotic density conjecture. … The conjecture predicts the limiting density of the…

Let $n$ be an odd positive integer, and let $\xi(n)$ denote the toroidal covering parameter. Multiplicative reduction conjecture. … This conjecture proposes an exact reduction of t…