PHASE TRANSITIONS IN INFINITELY GENERATED GROUPS, AND RELATED PROBLEMS IN ADDITIVE NUMBER THEORY

摘要

Let A be an infinite set of generators for a group G, and let LA(r) denote the number of elements of G whose word length with respect to A is exactly r. The growth function LA is a function from the nonnegative integers N0 to the set N0 ∪ {∞}. The purpose of this note is to determine all growth functions associated to infinite generating sets for groups.