  The one-dimensional Bose-Hubbard model in large-$U$ limit has been studied
via reducing and mapping the Hamiltonian to a simpler one. The eigenstates and
eigenvalues have been obtained exactly in the subspaces with fixed numbers of
single- and double-occupancies but without multiple-occupancies, and the
thermodynamic properties of the system have been calculated further. These
eigenstates and eigenvalues also enable us to develop a new perturbation
treatment of the model, with which the ground-state energy has been calculated
exactly to first order in $1/U$.
