Triangle-Free Triangulations

Abstract

The flip operation on colored inner-triangle-free triangulations of a convex polygon is studied. It is shown that the affine Weyl group $\widetilde{C}_n$ acts transitively on these triangulations by colored flips, and that the resulting colored flip graph is closely related to a lower interval in the weak order on $\widetilde{C}_n$. Lattice properties of this order are then applied to compute the diameter.