2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73859This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective dimension of these ideals, which turns out to be a new numerical invariant of forests. Finally, we propose a possible extension of this invariant to general graphs.12 pagesCommutative AlgebraCombinatorics13F55; 13D02; 05C05; 05E99text