Proof of Nonexistence of a Specific Difference Set
Published:Dec 31, 2025 03:36
•1 min read
•ArXiv
Analysis
This paper solves a 70-year-old open problem in combinatorics by proving the nonexistence of a specific type of difference set. The approach is novel, utilizing category theory and association schemes, which suggests a potentially powerful new framework for tackling similar problems. The use of linear programming with quadratic constraints for the final reduction is also noteworthy.
Key Takeaways
- •Proves the nonexistence of a specific difference set.
- •Employs a novel categorical approach using association schemes.
- •Utilizes linear programming with quadratic constraints for the final proof.
- •Addresses a long-standing open problem in combinatorics.
Reference
“We prove the nonexistence of $(120, 35, 10)$-difference sets, which has been an open problem for 70 years since Bruck introduced the notion of nonabelian difference sets.”