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arXiv · 1312.0502

On the two-point function of general planar maps and hypermaps

Jérémie Bouttier·Éric Fusy·Emmanuel Guitter
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Abstract

We consider the problem of computing the distance-dependent two-point function of general planar maps and hypermaps, i.e. the problem of counting such maps with two marked points at a prescribed distance. The maps considered here may have faces of arbitrarily large degree, which requires new bijections to be tackled. We obtain exact expressions for the following cases: general and bipartite maps counted by their number of edges, 3-hypermaps and 3-constellations counted by their number of dark faces, and finally general and bipartite maps counted by both their number of edges and their number of faces.

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Jérémie Bouttier, Éric Fusy, Emmanuel Guitter. 2013-12-02. On the two-point function of general planar maps and hypermaps. https://doi.org/10.4171/aihpd/8

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