  We investigate the polygamy relations related to the concurrence of
assistance for any multipartite pure states. General polygamy inequalities
given by the $\alpha$th $(0\leq \alpha\leq 2)$ power of concurrence of
assistance is first presented for multipartite pure states in
arbitrary-dimensional quantum systems. We further show that the general
polygamy inequalities can even be improved to be tighter inequalities under
certain conditions on the assisted entanglement of bipartite subsystems. Based
on the improved polygamy relations, lower bound for distribution of bipartite
entanglement is provided in a multipartite system. Moreover, the $\beta$th
($0\leq \beta \leq 1$) power of polygamy inequalities are obtained for the
entanglement of assistance as a by-product, which are shown to be tighter than
the existing ones. A detailed example is presented.
