  By means of the Lanczos method we analyze superconducting correlations in
ultrasmall grains at fixed particle number. We compute the ground state
properties and the excitation gap of the pairing Hamiltonian as a function of
the level spacing $\delta$. Both quantities turn out to be parity dependent and
universal functions of the ratio $\delta/\Delta$ ($\Delta$ is the BCS gap). We
then characterize superconductivity in the canonical ensemble from the scaling
behavior of correlation functions in energy space.

Superconductivity;Mesoscale and Nanoscale Physics