Codimensions of algebras and growth functions

Let A be an algebra over a field F of characteristic zero and let c(n) (A), n = 1, 2,..., be its sequence of codimensions. We prove that if c(n) (A) is exponentially bounded, its exponential growth can be any real number > 1. This is achieved by constructing, for any real number alpha > 1, an F-algebra A(alpha) such that lim(n ->infinity) (n)root c(n)(A alpha) exists and equals alpha. The methods are based on the representation theory of the symmetric group and on properties of infinite Sturmian and periodic words. (c) 2007 Elsevier Inc. All rights reserved.