On Generalized h -Vectors of Rational Polytopes with a Symmetry of Prime Order

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.