# Progress on the result about montonicity of Kazhdan Lustzig polynomials

I am reading the paper Masato Kobayashi---Combinatorics on Bruhat Graphs and Kazhdan-Lusztig Polynomials.

Let $$P_{x,w}$$ be the Kazhdan Lusztig polynomial of $$W$$. There is a result about crystallographic Coxeter group $$W$$:

I would like to know whether there is any generalization of this result to a larger class of Coxeter groups which has been proven up to now?

• Keep in mind the fact that the known result aready covers all cases in which the group is a "Weyl group", though your question is a natural one to raise. (By the way, I just expanded the tags and fixed a couple of small linguistic errors.) Sep 19, 2019 at 12:47