Mixed-type reverse-order laws of (AB)(1,3),(AB)(1,2,3)(AB)(1,3),(AB)(1,2,3) and (AB)(1,3,4)(AB)(1,3,4)

In this paper, by using the extremal ranks of generalized Schur complements, we study the mixed-type reverse-order laws for (AB)(1,3),(AB)(1,2,3)(AB)(1,3),(AB)(1,2,3) and (AB)(1,3,4)(AB)(1,3,4), and the sufficient and necessary conditions are established for these reverse-order laws.