A Generalisation on Erdős Distinct Subset Sums Problem

2025/10/07 by Zhengyu Gu, Gu, Zijie
Mathematics · #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2510.06032

Abstract

This paper investigates the Erdős distinct subset sums problem in ℤ^k. Beyond the classical variance method, using alternative statistical quantities like 𝔼[‖X‖₁] and 𝔼[‖X‖₃³] can yield better bounds in certain dimensions. This innovation improves previous low-dimensional results and provides a framework for choosing suitable methods depending on the dimension.

Citations

• Variations on the Erdős distinct-sums problem
• Siegel's Lemma and Sum-Distinct Sets

Related

• Variants of the Erdős distinct sums problem and variance method
• A note on the Erdős distinct subset sums problem
• Variations on the Erdős distinct-sums problem
• The Erdős distinct subset sums problem in a modular setting
• Some Remarks on the Erdős Distinct Subset Sums Problem