Denominator bounds for higher order systems of linear recurrence equations

Let (K, σ) be a difference field. We define the set of constants by const K = {c ∈ K | σ(c) = c}. A ΠΣ*-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 (Π case) or σ(t) = t + b (Σ* case) for some non-zero a or b ∈ K such that const K(t) = const K holds. See, for example, [8, 9] for more details on ΠΣ*-extensions.