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arXiv · 2506.23499

Unbounded knapsack problem and double partitions

Boris Y. Rubinstein
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Abstract

The unbounded knapsack problem can be considered as a particular case of the double partition problem that asks for a number of nonnegative integer solutions to a system of two linear Diophantine equations with integer coefficients. In the middle of 19th century Sylvester and Cayley suggested an approach based on the variable elimination allowing a reduction of a double partition to a sum of scalar partitions. This manuscript discusses a geometric interpretation of this method and its application to the knapsack problem.

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Boris Y. Rubinstein. 2025-06-30. Unbounded knapsack problem and double partitions. https://arxiv.org/abs/2506.23499

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