  We call {\it monomer} a B-DNA base-pair and examine, analytically and
numerically, electron or hole oscillations in monomer- and dimer-polymers,
i.e., periodic sequences with repetition unit made of one or two monomers. We
employ a tight-binding (TB) approach at the base-pair level to readily
determine the spatiotemporal evolution of a single extra carrier along a $N$
base-pair polymer. We study HOMO and LUMO eigenspectra as well as the mean over
time probabilities to find the carrier at a particular monomer. We use the pure
mean transfer rate $k$ to evaluate the easiness of charge transfer. The inverse
decay length $\beta$ for exponential fits $k(d)$, where $d$ is the charge
transfer distance, and the exponent $\eta$ for power law fits $k(N)$ are
computed; generally power law fits are better. We illustrate that increasing
the number of different parameters involved in the TB description, the fall of
$k(d)$ or $k(N)$ becomes steeper and show the range covered by $\beta$ and
$\eta$. Finally, both for the time-independent and the time-dependent problem,
we analyze the {\it palindromicity} and the {\it degree of eigenspectrum
dependence} of the probabilities to find the carrier at a particular monomer.
