  Markov matrices of equal-input type constitute a widely used model class. The
corresponding equal-input generators span an interesting subalgebra of the real
matrices with zero row sums. Here, we summarise some of their amazing
properties and discuss the corresponding Markov embedding problem, both
homogeneous and inhomogeneous in time. In particular, we derive exact and
explicit solutions for time-inhomogeneous Markov flows with non-commuting
generator families of equal-input type and beyond.
