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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-Lusztigpolynomials $ \left \{ P_{x,y} \mid x,y\in E_J\right \}$. In this paper, westudy the combinatorial formulas for $P_{x,y}$, which will extend the resultsof Brenti [2] and Deodhar [5].

Combinatorial formulas for Kazhdan-Lusztig polynomials with respect to W-graph ideals