We compute the reverse lexicographic generic initial ideals of the powers of a 2-complete intersection ideal I. In particular, we give six algorithms to compute these generic initial ideals, the choice of which depends on the power and on the relative degrees of the minimal generators of I. 1 arXiv:1206.5750v2 [math.AC] 30 Sep 2012 λ nα−1 = β − α + 1.Note that we can write λ 0 and λ k−1 in terms of l := β − α and α as follows:3.2. The Hilbert function of gin(I n ). The following result tells us that the invariants of gin(I n ) are completely determined by H gin(I n ) (t); this observation will be the key to computing these invariants.Lemma 3.6. Suppose that we have an ideal J of the formwhere the µ i s are strictly decreasing. If H J (t) = H I n (t) for a type (α, β) complete intersection ideal I then gin(I n ) = J.This lemma is an immediate consequence of the following well-known result. Although it is used in the literature (for example, it has the same content as Lemma 4.2 of [Gre98]), we record a complete proof here. 8 SARAH MAYES Lemma 3.7. An ideal of the form J = (x k , x k−1 y λ k−1 , . . . , xy λ 1 , y λ 0 )where λ 0 > λ 1 > · · · > λ k−1 is uniquely determined by its Hilbert function.Proof. The key observation here is thatis the Hilbert function of an ideal J as in the statement of the lemma.First note that x k is the smallest degree element of J so that k = min{t|H J (t) = 0}.Consider the ideal L k = (x k ) ⊂ J and its Hilbert function H L k (t). Set S k = min{t|H J (t) = H L k (t)} so that the smallest degree monomial that is in J but not in L k is of degree