Year: 2026
Type: preprint
Abstract: We give a self-contained elementary proof of the known result that every set $A\subset\R$ of cardinality seven satisfies $|A+A|\le |A-A|$. The argument adapts Hegarty's method, using representation counts and the largest positive differences. An exact counting identity, two applications of the Cauchy--Schwarz inequality, and an analysis of a symmetric six-element set with one point added complete the proof, with no computer enumeration. This answers in the affirmative a question of Chu for the seven-element case.
Source: arXiv (Cornell University)
Authors: Do, Thai Duong, Nguyen, Van Thien
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214959211