diff --git a/main.tex b/main.tex index 2eb42b590553297d994cd9f04f5d36a4c9c0f9d9..942929704d2e75ab752be2cec93f087864753df3 100644 --- a/main.tex +++ b/main.tex @@ -721,7 +721,7 @@ The following Lemma says that if a set $S$ splits the graph in two, then those t \cdots \P^{G\setminus Y}_S(\xi^{G\setminus Y}) \; \P^{G\setminus X}_S(\xi^{G\setminus X}) \tag{definition} \\ - &= (1-p_{1,1}) \; p_{1,2} \; p_{2,2} \; (1-p_{3,2}) \; \P^{G\setminus Y}_S(\xi^{G\setminus Y}) \; \P^{G\setminus X}_S(\xi^{G\setminus X}) + &= (1-p_{1,1}) \; p_{1,2} \; p_{2,2} \; (1-p_{3,2}) \cdots \P^{G\setminus Y}_S(\xi^{G\setminus Y}) \; \P^{G\setminus X}_S(\xi^{G\setminus X}) \tag{definition of $p_{i,j}$} \\ &= \P(\text{path in grid}) \; \P^{G\setminus Y}_S(\xi^{G\setminus Y}) \; \P^{G\setminus X}_S(\xi^{G\setminus X}) \end{align*}