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The distance-dependent two-point function of triangulations: a new derivation from old results. (English) Zbl 1379.05029
The article recalls the definition of slices and their connection with the distance-dependent two-point function of random planar triangulations, and the standard integrable system obeyed by the slice generating functions. A section is dedicated to the derivation of a new recursion relation between the generating function $$T_k$$ for slices with (maximum) border length $$k$$ and $$T_{k-1}$$. A study about simple triangulations is done in Section 4, and then it is used in the case of the explicit Tutte form for the kernel of the recursion relation to rewrite in a particularly simple and classical form. Explicit expressions for $$T_k$$ and for the distance-dependent two point function are given in Section 6. Some concluding remarks are given in Section 7.

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory 05A15 Exact enumeration problems, generating functions
##### Keywords:
planar maps; triangulations; two-point function; hull
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