Unbounded knapsack problem and double partitions
Number Theory
2025-07-01 v1 Cryptography and Security
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.
Cite
@article{arxiv.2506.23499,
title = {Unbounded knapsack problem and double partitions},
author = {Boris Y. Rubinstein},
journal= {arXiv preprint arXiv:2506.23499},
year = {2025}
}
Comments
6 pages, 1 figure