  We prove that the combinatorial invariance conjecture for parabolic
Kazhdan-Lusztig polynomials, formulated by Mario Marietti, is equivalent to its
restriction to maximal quotients. This equivalence lies at the other extreme in
respect to the equivalence, recently proved by Barkley and Gaetz, with the
invariance conjecture for Kazhdan-Lusztig polynomials, which turns out to be
equivalent to the conjecture for maximal quotients.
