  Hecke symmetries generalize the usual tensor symmetry of vector spaces
$v\otimes w\arrow w\otimes v$ as well as the symmetry of vector superspaces. To
a Hecke symmetry $R$ there associates a quadratic algebra which can be
interpreted as the function algebra upon a certain quantum space. This paper
investigates the Poincare series of this quadratic algebra. We showthat it is a
rational function with numerator and denominator being a reciprocal polynomial
and a skew-reciprocal polynomial, respectively.
