2 problems

Let $\mathbb T_n:=\mathbb Z^2/n\mathbb Z^2$, and let $A_n$ be the event that there is an open circuit with non-trivial homotopy in $\mathbb T_n$. For an edge $e$, write…

Let $\mathbb T_n:=\mathbb Z^2/n\mathbb Z^2$, and let $A_n$ be the event that there is an open circuit with non-trivial homotopy in $\mathbb T_n$. For an edge $e$, write…