  In order to better understand the fundamental issue regarding the
compatibility between the quark-shell picture and that of resonances in
meson-nucleon scattering in large $N_c$ QCD we extend the work of Cohen and
Lebed on mixed symmetric $\ell $ = 1 baryons to analyze excited states with
$\ell $ = 3. We give an explicit proof on the degeneracy of mass eigenvalues of
a simple Hamiltonian including operators up to order $\mathcal{O}(N^0_c)$
\emph{i. e.} neglecting $1/N_c$ corrections in the quark-shell picture in the
large $N_c$ limit. We obtain three degenerate multiplets formed of $\ell = 3$
states, as in the case of $\ell $ = 1 baryons. The compatibility between this
picture and that of resonances in meson-nucleon scattering is discussed in the
light of the present results.
