Polynomial entropy on the n-fold symmetric product and its suspension

We prove that the polynomial entropy of the induced map Fₙ(f) on the n-fold symmetric product of a compact space X and its suspension are both equal to nhₚₒₗ(f), when f:X→ X is a homeomorphism with a finite non-wandering set $NW(f)$. We also give a lower bound for the polynomial entropy on the suspension, for a homeomorphism f with at least one wandering point, under certain assumptions.