Using equidistribution criteria, we establish divisibility by cyclotomic polynomials of several partition interest, including spt-crank, overpartition pairs, and t-core partitions. As corollaries, obtain new proofs various Ramanujan-type congruences for associated functions. Moreover, using results Erdös Turán, the roots on unit circle those rank, crank, spt, unimodal sequences. Our complement ...

A common approach to scaling transactional databases in practice is horizontal partitioning, which increases system scalability, high availability and self-manageability. Usually it is very challenging to choose or design an optimal partitioning scheme for a given workload and database. In this technical report, we propose a fine-grained hyper-graph based database partitioning system for transa...