English

On the structures of subset sums in higher dimension

Combinatorics 2024-06-07 v2 Number Theory

Abstract

A given subset AA of natural numbers is said to be complete if every element of N\N is the sum of distinct terms taken from AA. 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