  We present an exploratory study of structure of 13C, 15C, 17C and
  19C, showing that the simple one-quasiparticle projected BCS
  (PBCS) model is capable to account for several important properties of these
nuclei. Next we discuss the importance of the Pauli Principle in the
particle-core models of normal-parity states in 13C and 11Be. This is done by
considering the pairing interaction between nucleons moving in an over-all
deformed potential. To assess the importance of pairing correlations in these
light nuclei we use both the simple BCS and the PBCS approximations. We show
that the Pauli Principle plays a crucial role in the parity inversion in 11Be.
It is also found that the effect of the particle number conservation in
relatively light and/or exotic nuclei is quite significant.
  Comparison of our results with several recent papers on the same subject, as
well as with some experimental data, is presented.
