2021/10/07 by Lev, Vsevolod F.
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2110.03554
Merging together a result of Nathanson from the early 70s and a recent result of Granville and Walker, we show that for any finite set A of integers with min(A)=0 and gcd(A)=1 there exist two sets, the "head" and the "tail", such that if m≥max(A)-|A|+2, then the m-fold sumset mA consists of the union of these sets and a long block of consecutive integers separating them. We give sharp estimates for the length of the block, and investigate the corresponding stability problem classifying those sets A for which the bound max(A)-|A|+2 cannot be substantially improved.