On the structures of subset sums in higher dimension
Combinatorics
2024-06-07 v2 Number Theory
Abstract
A given subset of natural numbers is said to be complete if every element of is the sum of distinct terms taken from . This topic is strongly connected to the knapsack problem which is known to be NP complete. The main goal of the paper is to study the structure of subset sums in a higher dimension. We show 'dense' sets and generalized arithmetic progrssions in subset sums of certain sets.
Keywords
Cite
@article{arxiv.2405.02269,
title = {On the structures of subset sums in higher dimension},
author = {Norbert Hegyvári and Máté Pálfy and Erfei Yue},
journal= {arXiv preprint arXiv:2405.02269},
year = {2024}
}
Comments
22 pages, Minor correction to the title and in the proof of Proposition 1.1