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The number of rooted maps on an orientable surface. (English) Zbl 0751.05052
Authors’ abstract: Let $$m_ g(n)$$ be the number of rooted $$n$$ edged maps on an orientable surface of genus $$g>0$$. The generating function of $$\rho=(1-12x)^{1/2}$$ whose denominator factors completely into powers of $$\rho$$, $$\rho+2$$, and $$\rho+5$$. We calculate $$M_ 2(x)$$ and $$M_ 3(x)$$. Unfortunately, we have not been able to discern a pattern in the sequence $$M_ g(x)$$ from the values for $$g\leq 3$$.

##### MSC:
 05C30 Enumeration in graph theory
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