  As shown in previous work, number projection can be carried out analytically
for states defined in a quasi-particle scheme when the states are expressed in
a coherent state representation. The wave functions of number-projected states
are well-known in the theory of orthogonal polynomials as Schur functions.
Moreover, the functions needed in pairing theory are a particularly simple
class of Schur functions that are easily constructed by means of recursion
relations. It is shown that complete sets of states can be projected from
corresponding quasi-particle states and that such states retain many of the
properties of the quasi-particle states from which they derive. It is also
shown that number projection can be used to construct a complete set of
orthogonal states classified by generalized seniority for any nucleus.
