2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126978Let Z be a finite set of double points in P^1 x P^1 and suppose further that X, the support of Z, is arithmetically Cohen-Macaulay (ACM). We present an algorithm, which depends only upon a combinatorial description of X, for the bigraded Betti numbers of I_Z, the defining ideal of Z. We then relate the total Betti numbers of I_Z to the shifts in the graded resolution, thus answering a special case of a question of T. Roemer.20 pages; revised version includes more detailed proofs in Section 4, and a new section (Section 6) where we answer a special case of question of T. Roemer. To appear J. Pure Appl. AlgCommutative AlgebraAlgebraic Geometry13D40, 13D02, 13H10, 14A15text