English

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

Combinatorics 2015-07-21 v1 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.1312.0502,
  title  = {On the two-point function of general planar maps and hypermaps},
  author = {Jérémie Bouttier and Éric Fusy and Emmanuel Guitter},
  journal= {arXiv preprint arXiv:1312.0502},
  year   = {2015}
}

Comments

32 pages, 17 figures

R2 v1 2026-06-22T02:19:01.215Z