2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77158We 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 R.~Stanley and R.~Adin for the $h$--vector of a simplicial rational polytope with a central symmetry or a symmetry of prime order respectively.10 pages, TeX, to appear in Discrete Comput. GeomAlgebraic GeometryCombinatorics52B20, 14M25, 14F32text