On stable embeddability of partitions

Several natural partial orders on integral partitions, such as the embeddability, the stable embeddability, the bulk embeddability and the supermajorization, arise in quantum computation, bin-packing and matrix analysis. We find the implications of these partial orders. For integral partitions whose entries are all powers of a fixed number pp, we show that the embeddability is completely determined by the supermajorization order and we find an algorithm for determining the stable embeddability.