The generic rigidity conjecture for k-triangulations

A $k$-triangulation is a maximal set of pairwise noncrossing diagonals of a convex polygon in which no $k+1$ diagonals mutually cross. A graph is generically minimally rigid in dimension $d$ if a generic embedding of its vertices in $d$-dimensional Euclidean space is minimally rigid. Generic rigidity conjecture. Every $k$-triangulation is generically minimally rigid in dimension $2k$. The conjecture extends the Laman characterization of generic minimal rigidity in the plane; the paper proves it for $k=2$, while the general case remains open.