Computational Aspects of Ordered Integer Partition with Upper Bounds
We propose a novel algorithm for computing the number of ordered integer partitions with upper bounds. This problem’s task is to compute the number of distributions of z balls into n urns with constrained capacities \(i_1,\hdots,i_n\) (see ). Besides the fact that this elementary urn problem has no known combinatoric solution, it is interesting because of its applications in the theory of database preferences as described in  and . The running time of our algorithm depends only on the number of urns and not on their capacities as in other previously known algorithms.
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