Progression-free sets in Z_4^n are exponentially small

21 May 2016 · Croot Ernie, Lev Vsevolod, Pach Peter ·

We show that for integer $n>0$, any subset $A \subset Z_4^n$ free of three-term arithmetic progressions has size $|A| < 4^{c n}$, with an absolute constant $c \approx 0.926$.