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We propose a method to challenge the calculation of genus-$g$, bulk$n$-point, $b$-boundary, $c$-crosscap correlation functions with $x$ boundaryoperators $\mathcal{F}_{g,n,b,c}^{x}$ in two-dimensional conformal fieldtheories (CFT$_2$). We show that $\mathcal{F}_{g,n,b,c}^{x}$ are infinitelinear combinations of genus-$g$, bulk $(n+b+c)$-point functions$\mathcal{F}_{g,(n+b+c)}$, and try to obtain the linear coefficients in thiswork. We show the existence of a single pole structure in the linearcoefficients at degenerate limits. A practical method to obtain the infinitelinear coefficients is the free field realizations of Ishibashi states. Wereview the results in Virasoro minimal models $\mathcal{M}(p,p')$ and extend itto the $N=1$ minimal models $\mathcal{SM}(p,p')$.

The linear property of genus-$g$, $n$-point, $b$-boundary, $c$-crosscap correlation functions in two-dimensional conformal field theory