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Ramified coverings of \(S^ 2\) with one degenerate branching point and enumeration of edge-ordered graphs. (English) Zbl 0883.05072
Khovanskij, A. (ed.) et al., Topics in singularity theory. V. I. Arnold’s 60th anniversary collection. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 180(34), 219-227 (1997).
From the authors’ abstract: In this short note we extend the results of Lyashko, Looijenga, and Arnold on the number of nonequivalent rational functions on the sphere with 1 or 2 poles and simple finite branching points to several other cases. In particular, we calculate the number of meromorphic functions on the torus with the same properties.
For the entire collection see [Zbl 0870.00037].

05C30 Enumeration in graph theory
30F10 Compact Riemann surfaces and uniformization