Research Paper#Additive Combinatorics, Extremal Set Theory, Finite Fields🔬 ResearchAnalyzed: Jan 3, 2026 19:31
Hilton-Milner Results for (k, ℓ)-Sum-Free Sets in Finite Vector Spaces
Published:Dec 28, 2025 08:27
•1 min read
•ArXiv
Analysis
This paper extends the Hilton-Milner theory to (k, ℓ)-sum-free sets in finite vector spaces, providing a deeper understanding of their structure and maximum size. It addresses a problem in additive combinatorics, offering stability results and classifications beyond the extremal regime. The work connects to the 3k-4 conjecture and utilizes additive combinatorics and Fourier analysis, demonstrating the interplay between different mathematical areas.
Key Takeaways
- •Provides a general Hilton-Milner theory for (k, ℓ)-sum-free sets.
- •Determines the maximum size and extremal configurations for these sets.
- •Proves sharp stability results beyond the extremal regime.
- •Applies additive combinatorics and Fourier-analytic methods.
- •Highlights connections to the 3k-4 conjecture.
Reference
“The paper determines the maximum size of (k, ℓ)-sum-free sets and classifies extremal configurations, proving sharp Hilton-Milner type stability results.”