Catalan numbers and branched coverings by the Riemann sphere

@article{Goldberg1991CatalanNA,
  title={Catalan numbers and branched coverings by the Riemann sphere},
  author={L. Goldberg},
  journal={Advances in Mathematics},
  year={1991},
  volume={85},
  pages={129-144}
}
  • L. Goldberg
  • Published 1991
  • Mathematics
  • Advances in Mathematics
We prove that the number of PGL(2, C) equivalence classes of degree d rational maps with a fixed branch set is generically equal to the “Catalan number” ϱ(d) = (1d)(2d−2d−1). Several (previously known) applications of Catalan numbers to combinatorics and algebraic geometry are discussed throughout the course of the article. 
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References

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