In view of the recursive equation \(\mathbf{p}^{(n)}=\mathbf{p}^{(n-1)} \cdot T\) for the short-run distributions of a Markov chain, assuming that there is such a thing as a long-run or limiting distribution represented by a vector \(\mathbf{p}\), what equation should that vector satisfy? Check your hypothesis against the computations of Examples 1 and 3 in Section 4.2 on the frozen food companies.