Long arithmetic progressions in sumsets: Thresholds and Bounds

E. Szemeredi, V. Vu

For a set $A$ of integers, the sumset $lA=A+...+A$ consists of those numbers which can be represented as a sum of $l$ elements of $A$ $$lA=\{a_1+...a_l|a_i\in A_i\}.$$ A clo…