  We survey the matrix product solutions of the Yang-Baxter equation obtained
recently from the tetrahedron equation. They form a family of quantum $R$
matrices of generalized quantum groups interpolating the symmetric tensor
representations of $U_q(A^{(1)}_{n-1})$ and the anti-symmetric tensor
representations of $U_{-q^{-1}}(A^{(1)}_{n-1})$. We show that at $q=0$ they all
reduce to the Yang-Baxter maps called combinatorial $R$, and describe the
latter by explicit algorithm.
