Quivers, long exact sequences and Horn type inequalities II

We study the set of all m-tuples $(\lambda(1),...,\lambda(m))$ of possible types of finite abelian p-groups $M_{\lambda(1)}, ..., M_{\lambda(m)}$ for which there exists a long exact sequence $M_{\lambda(1)} \to ... \to M_{\lambda(m)}$. When m=3, we recover Fulton's results on the possible eigenvalues of majorized Hermitian matrices.