On the two-point function of general planar maps and hypermaps
Annales de l’Institut Henri Poincaré D, Tome 1 (2014) no. 3, pp. 265-306.

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.

Accepté le :
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DOI : 10.4171/aihpd/8
Classification : 05-XX, 52-XX, 60-XX, 82-XX
Mots-clés : random geometry, maps, graph distance, two-point function, discrete integrability, bijections, enumerative combinatorics 
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     title = {On the two-point function of general planar maps and hypermaps},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {265--306},
     volume = {1},
     number = {3},
     year = {2014},
     doi = {10.4171/aihpd/8},
     mrnumber = {3239273},
     zbl = {1301.05079},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/aihpd/8/}
}
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Bouttier, Jérémie; Fusy, Éric; Guitter, Emmanuel. On the two-point function of general planar maps and hypermaps. Annales de l’Institut Henri Poincaré D, Tome 1 (2014) no. 3, pp. 265-306. doi : 10.4171/aihpd/8. http://www.numdam.org/articles/10.4171/aihpd/8/

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