and similar for $\xi^{G\setminus X}$.

    Instead of choosing a step in $Y,X,X,Y,\cdots$ we could have chosen other orderings. The following diagram illustrates all possible interleavings, and the red line corresponds to the particular interleaving $Y,X,X,Y$ in the example above.

    \begin{center}

    \end{center}

    For the labels shown within the grid, define $p_{ij} = \frac{z^X_i}{z^X_i + z^Y_j}$.

    The probability of this particular interleaving $\xi^G$ is given by