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] . [ABSTRACT FROM AUTHOR]