Let $A$ be a finite alphabet, let $p=(p_a)_{a\in A}$ be a probability vector on $A$, let $X=A^{\mathbb Z}$, let $\mu=p^{\mathbb Z}$, and let $T:X\to X$ be the shift map defined by $(Tx)_k=x_{k+1}$. If $\mathcal P=\{P_a:a\in A\}$ is the coordinate partition with $P_a=\{x\in X:x_0=a\}$, then $\mathcal P$ is a generator and