We prove tight lower bounds for the coefficients of the generalized
h -vector of a rational polytope with a symmetry of prime order that is fixed-point free on the boundary. These bounds generalize
results of Stanley and Adin for the
h -vector of a simplicial rational polytope with a central symmetry or a symmetry of prime order, respectively.
Received November 6, 1997, and in revised form March 17, 1998.