Maximizing the number of rational-value sums or zero-sums
Combinatorics
2025-09-25 v2 Number Theory
Abstract
What is the maximum number of -term sums admitting rational values in -element sets of irrational numbers? We determine the maximum when or and also in case when we drop the condition on the number of summands. It turns out that the -term sum problem is equivalent to determine the maximum number of -term zero-sum subsequences in -element sequences of integers, which can be seen as a variant of the famous Erd\H{o}s-Ginzburg-Ziv theorem.
Cite
@article{arxiv.2411.04449,
title = {Maximizing the number of rational-value sums or zero-sums},
author = {Benjamin Móricz and Zoltán Lóránt Nagy},
journal= {arXiv preprint arXiv:2411.04449},
year = {2025}
}