Breakthrough Tracker record
Erdős's large sum-free subset conjecture
Every n-element set of integers contains a sum-free subset of size at least n/3 + c log log n for an absolute positive c. The guaranteed excess over n/3 therefore tends to infinity.
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- Stable ID
math-erdos-large-sum-free-subsets-2025- Revision
math-erdos-large-sum-free-subsets-2025.v1- Field
- Mathematics · Additive combinatorics
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Current · Expert-supported preprint
- Last checked
AI role
No generative-AI role was disclosed.
Record details
- Problem or result
- Erdős's 1965 large sum-free subset conjecture
- Authors
- Benjamin Bedert
- Institutions
- University of Oxford at the time of the work
- Result date
- Preprint submitted February 12, 2025
Why it matters
The result settles a simple-to-state, 60-year-old problem connecting additive combinatorics and harmonic analysis.
Limits
The theorem proves an unbounded improvement of the stated order. It does not determine the optimal excess term.
Sources
- Primary: Benjamin Bedert, Large sum-free subsets of sets of integers
- Independent: Quanta, Graduate Student Solves Classic Problem About the Limits of Addition
Correction and revision history
- Added on 2026-07-22 with the unbounded-excess theorem distinguished from determination of the optimal term.
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