Eulerian triangulations: two-point function and hull perimeter statistics

We present a new derivation of the distance-dependent two-point function for planar Eulerian triangulations and give expressions for more refined generating functions where we also control hull perimeters. These results are obtained in the framework of a new recursion relation for slice generating functions and extend similar results obtained recently for triangulations and quadrangulations. A number of explicit formulas are given for the statistics of hull perimeters in infinitely large random planar Eulerian triangulations.