,$ let $S = \{s_k\},\ T = \{t_k\}$ be homogeneous LRS's with characteristic polynomials $\Phi_{0^n},\ \Phi_{r}$ respectively. Then as discussed earlier, the characteristic polynomial of $ST = \{s_k t_k \}$ is $\Phi_{0^nr} = \Phi_{0^n} \odot \Phi_r.$ S