Having some difficulty understanding the solution to this problem.
We have an action of $D_{2n}$ on set $A=\left\{{\left\{\overline{a},\overline{k+a}\right\}\mid1\leq a\leq k}\right\}$ and $s.\left\{\overline{a},\overline{k+a}\right\}=\overline{-a},\overline{-k-a}$ where geometrically $s$ flips the n-gon over the line passing through the vertices labelled $n$,$k$. Bars denote equivalence classes $\bmod n$.
I can't understand this since for $n=4$ that would map $(1,3)$ to $(-1,-3)$
However $1\neq-1\bmod4$ and $3\neq-3\bmod4$.
Please guys, help me understand what I'm doing wrong here..?
