LETTER TO THE EDITOR: Testing Hall-Post inequalities with exactly solvable N-body problems

The Hall-Post inequalities provide lower bounds on N-body energies in terms of N '-body energies with N ' < N. They are rewritten and generalized to be tested with exactly solvable models of Calogero-Sutherland type in one and higher dimensions. The bound for N spinless fermions in one dimension is better saturated at large coupling than for noninteracting fermions in an oscillator potential.