A proof of Erdős's B+B+t conjecture

2022/06/24 by Bryna Kra, Joel Moreira, Kra, Bryna +5 · 2 citations
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.2206.12377

Abstract

We show that every set A of natural numbers with positive upper density can be shifted to contain the restricted sumset \b₁ + b₂ : b₁, b₂∈ B and b₁ ≠ b₂ \ for some infinite set B ⊂ A.

Cited by

• Adherence Semigroups and Density Finite-Sums Configurations
• On density analogs of Hindman's finite sums theorem

Related

• Infinite unrestricted sumsets of the form B+B in sets with large density
• A short proof of a conjecture of Erdös proved by Moreira, Richter and Robertson
• Counterexamples to generalizations of the Erdős B+B+t problem
• Asymmetric infinite sumsets in large sets of integers
• The Density Finite Sums Theorem