Title: Combinatorial formulas for Kazhdan-Lusztig polynomials with respect to W-graph ideals,
Abstract: In \cite{y1} Yin generalized the definition of $W$-graph ideal $E_J$ in
weighted Coxeter groups and introduced the weighted Kazhdan-Lusztig polynomials
$ \left \{ P_{x,y} \mid x,y\in E_J\right \}$, where $J$ is a subset of simple
generators $S$. In this paper, we study the combinatorial formulas for those
polynomials, which extend the results of Deodhar \cite{v3} and Tagawa
\cite{h1}.