On maximal green sequences in abelian length categories

In this article, we study the relationship among maximal green sequences, complete forward hom-orthogonal sequences and stability functions in abelian length categories. Mainly, firstly give a one-to-one correspondence between via mutual constructions, then prove that sequence can be induced by central charge if only it satisfies crossing inequalities. As applications, show inequalities computed c -vectors for finite dimensional algebras; finally, Rotation Lemma Jacobian algebras.