  We investigate the conjectured ground state eigenvector of the 8-vertex model
inhomogeneous transfer matrix on its combinatorial line, i.e., at $\eta=\pi/3$,
where it acquires a particularly simple form. We compute the partition function
of the model on an infinite cylinder with certain restrictions on the
inhomogeneities, and taking the homogeneous limit, we obtain an expression for
the squared norm of the ground state of the XYZ spin chain as a solution of a
differential recurrence relation.
