2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154593This paper has been withdrawn since we combine this paper with math.AC/0503685. All contents of the paper have been moved to math.AC/0503685.This paper has been withdrawn. All contents of this paper have been moved to math.AC/0503685Commutative AlgebraCombinatorics13F55 (Primary); 13D02, 05E99 (Secondary)Combinatorial shifting and graded Betti numberstext