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Unbounded knapsack problem and double partitions
June 30, 2025 · Declared Dead · 🏛 arXiv.org
"No code URL or promise found in abstract"
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Authors
Boris Y. Rubinstein
arXiv ID
2506.23499
Category
math.NT
Cross-listed
cs.CR
Citations
0
Venue
arXiv.org
Last Checked
1 month ago
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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