Abstract The methods of group theory employed in previous articles of this series for particles in the 2s-1d shell are generalized to particles in the 2s-1d and holes in the 1p shell still considering that all single-particle states correspond to an harmonic oscillator common potential. We must then construct polynomials in creation operators for the particles and annihilation operators for the holes which are characterized by irreducible representation (IR) of a chain of groups. These IR will now have both positive and negative indices. The techniques for constructing the polynomials belonging to these IR are explicitly developed for all the groups in the chain. These polynomials are then applied to a physical vacuum state corresponding to an empty 2s-1d and filled 1p shells. As the physical vacuum state is not characterized by a scalar IR for all the groups in the chain, the application of the polynomials to it raises a problem of reduction of Kronecker products of IR of the groups in question which is explicitly solved. From the set of states we eliminate the spurious ones due to centre-of-mass motion. We then prove that for the remaining ones the model interaction introduced previously takes care appropriately of the short range, long range and spin orbit coupling correlations. With the help of the model interaction we discuss some examples and in particular the negative parity states of 18O, 18F.