A Burge tree of virasoro-type polynomial identities

Using a summation formula due to Burge, and a combinatorial identity betwee n partition pairs, we obtain an infinite tree of q-polynomial identities fo r the Virasoro characters chi(r,s)(p,p'), dependent on two finite sige para meters M and N, in the cases where: (1) p and p' are coprime integers that satisfy 0 < p < p'. (2) If the pair (p' :p) has a continued fraction (c(1), c(2),...,c(t-1), c( t) +2), where t greater than or equal to 1, then the pair (s:r) has a conti nued fraction (c(1),c(2),...,c(u-1), d), where 1 less than or equal to u le ss than or equal to t, and 1 less than or equal to d less than or equal to c(u). The limit M --> infinity, for fixed N, and the limit N --> infinity, for fi xed M, lead to two independent boson-fermion-type q-polynomial identities: in one case, the bosonic side has a conventional dependence on the paramete rs that characterize the corresponding character. In the other, that depend ence is not conventional. In each case, the fermionic side can also be cast in either of two different forms. Taking the remaining finite size parameter to infinity in either of the abo ve identities, so that M --> infinity and N --> infinity, leads to the same q-series identity for the corresponding character.