The distance-dependent two-point function of quadrangulations: a new derivation by direct recursion

TL;DR

This paper introduces a new recursive method to derive the distance-dependent two-point function of planar quadrangulations, extending techniques previously applied to triangulations, providing a novel analytical approach.

Contribution

The paper presents a new recursive derivation for the two-point function of quadrangulations, adapting methods from triangulations to quadrangulations.

Findings

Derived a new recursion relation for quadrangulations

Solved the recursion to obtain the two-point function

Extended recursive techniques from triangulations to quadrangulations

Abstract

We give a new derivation of the distance-dependent two-point function of planar quadrangulations by solving a new direct recursion relation for the associated slice generating functions. Our approach for both the derivation and the solution of this new recursion is in all points similar to that used recently by the author in the context of planar triangulations.