2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62700We describe new combinatorial methods for constructing an explicit free resolution of Z by ZG-modules when G is a group of fractions of a monoid where enough least common multiples exist (``locally Gaussian monoid''), and, therefore, for computing the homology of G. Our constructions apply in particular to all Artin groups of finite Coxeter type, so, as a corollary, they give new ways of computing the homology of these groups.Group TheoryK-Theory and Homology20J06, 18G35, 20M50, 20F36text