Valence sequences

Abstract

Let Vq, Vx.Vk,... be an infinite sequence of positive integers (where we include oo as a possible value for Vk). The sequence is called a valence sequence if there is an /(z) regular in the unit disk such that for each Ar > 0 the A:th derivative f-k\z) has valence Vk in E. Most of the results obtained here about valence sequences are obvious, but we prove three theorems about valence sequences that are not trivial.