Note on the Additive Basis Conjecture

2025/10/01 by Yu, Yang
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.01300

Abstract

We show that in a vector space over Z₃, the union of any four linear bases is an additive basis, thus proving the Additive Basis Conjecture for p=3, and providing an alternative proof of the weak 3-flow conjecture.

Citations

• Additive bases, coset covers, and non-vanishing linear maps
• On the additive bases problem in finite fields
• Additive Bases in Abelian Groups
• Coverings of abelian groups and vector spaces

Related

• Additive bases, coset covers, and non-vanishing linear maps
• Reduction of Rota's basis conjecture to a problem on three bases
• A metric for the set of all additive basis
• On Finitely Stable Additive Bases
• Additive bases arising from functions in a Hardy field