Denominator Bounds for Higher Order Systems of Linear Recurrence Equations

Let (K, σ) be a difference field. We define the set of constants by constK = {c ϵ K | σ (c) = c}. A IIΣ∗-extension of K is a field of rational functions K(t) over K together with an extension of σ to K(t) given by either σ(t) = at (II case) or σ(t) = t + b (Σ∗ case) for some non-zero a or b ϵ K such that constK(t) = constK holds. See, for example, [8, 9] for more details on IIΣ∗-extensions.