Supernomial coefficients, polynomial identities and q-series

q-Analogues of the coefficients of x(a) in the expansion of Pi(j=1)(N) (1 x +...+ x(j))L-j are proposed. Useful properties, such as recursion relati ons, symmetries and limiting theorems of the "q-supernomial coefficients" a re derived, and a combinatorial interpretation using generalized Durfee dis section partitions is given. Polynomial identities of boson-fermion-type, b ased on the continued fraction expansion of p/k and involving the q-superno mial coefficients, are proven. These include polynomial analogues of the An drews-Gordon identities. Our identities unify and extend many of the known boson-fermion identities for one-dimensional configuration sums of solvable lattice models, by introducing multiple finitization parameters.