Discrete Mathematics & Theoretical Computer Science 
We establish a simple recurrence formula for the number $Q_g^n$ of rooted orientable maps counted by edges and genus. The formula is a consequence of the KP equation for the generating function of bipartite maps, coupled with a Tutte equation, and it was apparently unnoticed before. It gives by far the fastest known way of computing these numbers, or the fixedgenus generating functions, especially for large $g$. The formula is similar in look to the one discovered by Goulden and Jackson for triangulations (although the latter does not rely on an additional Tutte equation). Both of them have a very combinatorial flavour, but finding a bijective interpretation is currently unsolved  should such an interpretation exist, the history of bijective methods for maps would tend to show that the case treated here is easier to start with than the one of triangulations.
Source : ScholeXplorer
IsRelatedTo ARXIV math/0004128 Source : ScholeXplorer IsRelatedTo DOI 10.4310/mrl.2000.v7.n4.a10 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/0004128
