On the additive bases problem in finite fields

2016/07/02 by Hatami, Hamed, de Quehen, Victoria · 1 citation
#11B13 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.00563

Abstract

We prove that if G is an Abelian group and A₁,…,A_k ⊆ G satisfy m A_i=G (the m-fold sumset), then A₁+…+A_k=G provided that k ≥ c_m log n. This generalizes a result of Alon, Linial, and Meshulam [Additive bases of vector spaces over prime fields. J. Combin. Theory Ser. A, 57(2):203--210, 1991] regarding the so called additive bases.

Cited by

• Note on the Additive Basis Conjecture

Related

• Additive Bases in Abelian Groups
• Generalized additive bases and difference bases for Cartesian product of finite abelian groups
• On additive bases of sets with small product set
• A Walk Through Some Newer Parts of Additive Combinatorics
• Sumsets of sequences in abelian groups and flags in field extensions