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Catalan numbers and branched coverings by the Riemann sphere

✍ Scribed by Lisa R Goldberg

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 601 KB
Volume: 85
Category: Article
ISSN: 0001-8708
DOI: 10.1016/0001-8708(91)90052-9

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✦ Synopsis

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" p(d) = (l/d)( 2j:f).

Several (previously known) applications of Catalan numbers to combinatorics and algebraic geometry are discussed throughout the course of the article.

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