The combinatorial invariance conjecture for parabolic Kazhdan-Lusztig polynomials of lower intervals

The aim of this work is to prove a conjecture related to the Combinatorial Invariance Conjecture of Kazhdan-Lusztig polynomials, in the parabolic setting, for lower intervals in every arbitrary Coxeter group. This result improves and generalizes, among other results, the main results of Brenti et al. (2006) [6], Marietti (2016) [21].