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. Explicit formulas are given for the statistics of hull perimeters in infinitely large random planar Eulerian triangulations.