On the number of pseudo-triangulations of certain point sets

We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it on two prominent families of point sets, namely the so-called double circle and double chain. The latter has asymptotically 12n nT(1) pointed pseudo-triangulations, which lies significantly above the maximum number of triangulations in a planar point set known so far.