Truncated path algebras and Betti numbers of polynomial growth

We investigate a class of truncated path algebras in which the Betti numbers of a simple module satisfy a polynomial of arbitrarily large degree. We produce truncated path algebras where the i-th Betti number of a simple module S is β_i(S) = i^k for 2 ≤ k ≤ 4 and provide a result of the existence of algebras where β_i(S) is a polynomial of degree 4 or less with nonnegative integer coefficients. In particular, we prove that this class of truncated path algebras produces Betti numbers corresponding to any polynomial in a certain family.