Eulerian triangulations: two-point function and hull perimeter statistics

TL;DR

This paper derives new formulas for the two-point function and hull perimeter statistics in large random planar Eulerian triangulations, extending previous work on related graph classes.

Contribution

It introduces a new recursion relation for slice generating functions to analyze Eulerian triangulations, providing refined statistical formulas.

Findings

Explicit formulas for hull perimeter statistics in large Eulerian triangulations

Extension of previous results from triangulations and quadrangulations

New recursion relation for slice generating functions

Abstract

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.