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The enumeration of maps and the study of uniform random maps have been classical topics of combinatorics and statistical physics ever since the seminal work of Tutte in the sixties. Following the bijective approach initiated by Cori and Vauquelin in the eighties, we describe a bijection between rooted maps, or rooted bipartite quadrangulations, on a surface… (More)
Different formulas counting families of non isomorphic chord diagrams are given : planar and toroidal ones and those of maximal genus. These formulas are obtained establishing results on the structure of the automorphism group of diagrams of a given genus.