Enumeration of almost polynomial rational functions with given critical values

1 Rational functions and minimal factorizations of permutations Let f : C C be a rational function of degree n in one complex variable. A critical point of f is a point z C such that f (z) = 0. Its degree is the number a 2 such that f looks like f(z) = za in the neighborhood of the critical point. A critical value of f is its value at a critical point. (Note that we do not count poles as critical points.)

• Type: Journal
• Year: 2008
• Where: EJC
• Authors: Dmitri Panov, Dimitri Zvonkine
• Keywords: Critical Points, EJC 2007, EJC 2008, Information Technology, Minimal Factorizations, Rational Function