Given a Schubert variety S contained in a Grassmannian Gk(Cl), we show how to obtain further information on the direct summands of the derived pushforward Rπ⁎QS˜ given by the application of the decomposition theorem to a suitable resolution of singularities π:S˜→S. As a by-product, Poincaré polynomial expressions are obtained along with an algorithm which computes the unknown terms in such expressions and which shows that the actual number of direct summands happens to be less than the number of supports of the decomposition.

The WiMAX 802.16e system is intended to support applications with challenging quality of service constraints in heterogeneous scenarios where both low and high mobility users are simultaneously active. However, the fast and deep channel fluctuations that are leveraged in rich scattering environments (i.e., urban scenarios) affect the performance of e.g., channel estimation, link adaptation and scheduling algorithms. Therefore, the physical and MAC layer algorithms need to be designed in order to support both low and high mobility users. Herein, the impact of users mobility on the design and the performance of the physical and MAC layers of a WiMAX base station is assessed, and suitable solutions for the channel estimation, dynamic link adaptation and scheduling algorithms are provided. Simulation results provide indications on the achievable maximum cell load for different mobility and QoS profiles. The optimal trade-off between the PUSC and AMC permutations is also numerically investigated.