The dihedral permutation-group size conjecture for indecomposable Yang–Baxter solutions

Let $X$ be an indecomposable solution of the Yang–Baxter equation whose permutation group is isomorphic to the dihedral group $D_{2n}$. Dihedral size conjecture. Then

$$|X|=2n.$$

For an indecomposable solution with permutation group $D_{2n}$, the preceding result shows that its size can only be $n$ or $2n$; the conjecture asserts that the first possibility never occurs. It is supported in the paper by the classification for permutation group $D_{4p}$, where all indecomposable solutions have size $4p$.