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Annales de l’Institut Henri Poincaré D

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Volume 6, Issue 1, 2019, pp. 1–42
DOI: 10.4171/AIHPD/62

Published online: 2018-07-25

Eulerian triangulations: two-point function and hull perimeter statistics

Emmanuel Guitter[1]

(1) Université Paris Saclay, Gif-sur-Yvette, France

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.

Keywords: Planar maps, Eulerian triangulations, two-point function, hull perimeter

Guitter Emmanuel: Eulerian triangulations: two-point function and hull perimeter statistics. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), 1-42. doi: 10.4171/AIHPD/62