Abstract
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 p , we show that the embeddability is completely determined by the supermajorization order and we find an algorithm for determining the stable embeddability.
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