  Let $(W,S,L)$ be a weighted Coxeter system and $J$ a subset of $S$, Yin [12]
introduced the weighted $W$-graph ideal $E_J$ and the weighted Kazhdan-Lusztig
polynomials $ \left \{ P_{x,y} \mid x,y\in E_J\right \}$. In this paper, we
study the combinatorial formulas for $P_{x,y}$, which will extend the results
of Brenti [2] and Deodhar [5].
