Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
401151 | Journal of Symbolic Computation | 2015 | 14 Pages |
Abstract
Given a set of integers W, the Partition problem determines whether W can be divided into two disjoint subsets with equal sums. We model the Partition problem as a system of polynomial equations, and then investigate the complexity of a Hilbert's Nullstellensatz refutation, or certificate, that a given set of integers is not partitionable. We provide an explicit construction of a minimum-degree certificate, and then demonstrate that the Partition problem is equivalent to the determinant of a carefully constructed matrix called the partition matrix. In particular, we show that the determinant of the partition matrix is a polynomial that factors into an iteration over all possible partitions of W.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
S. Margulies, S. Onn, D.V. Pasechnik,