2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100908We give necessary and sufficient inequalities for the existence of long exact sequences of m finite abelian p-groups with fixed isomorphy types. This problem is related to some generalized Littlewood-Richardson coefficients that we define in this paper. We also show how this problem is related to eigenvalues of Hermitian matrices satisfying certain (in)equalities. When m=3, we recover the Horn type inequalities that solve the saturation conjecture for Littlewood-Richardson coefficients and Horn's conjecture.29 pagesRepresentation TheoryCombinatorics16G20; 05E15text