Enumeration of Planar Rooted Triangulations

We illustrate two basic techniques on enumerating rooted maps by reviewing Tutte's results on 3-connected and 4-connected triangulations. We then show how to combine the two techniques to enumerate 5-connected triangulations. It will be shown that the 5-connected case is much more complicated than the 3- and 4-connected cases and Maple is used heavily to solve the problem.