  We study theoretically the transmission properties of serially connected
mesoscopic rings threaded by a magnetic flux. Within a tight-binding formalism
we derive exact analytical results for the transmission through periodic and
quasiperiodic Fibonacci arrays of rings of two different sizes. The role played
by the number of scatterers in each arm of the ring is analyzed in some detail.
The behavior of the transmission coefficient at a particular value of the
energy of the incident electron is studied as a function of the magnetic flux
(and vice versa) for both the periodic and quasiperiodic arrays of rings having
different number of atoms in the arms. We find interesting resonance properties
at specific values of the flux, as well as a power-law decay in the
transmission coefficient as the number of rings increases, when the magnetic
field is switched off. For the quasiperiodic Fibonacci sequence we discuss
various features of the transmission characteristics as functions of energy and
flux, including one special case where, at a special value of the energy and in
the absence of any magnetic field, the transmittivity changes periodically as a
function of the system size.
