DETAILED STRUCTURE FOR FREIMAN’S 3k 3 THEOREM

摘要

Let A be a set of k integers. We study Freiman’s inverse problem with small doublings and continue the work of G. A. Freiman, I. Bardaji and D. J. Grynkiewicz by characterizing the detailed structure of A in Theorem 2.2 below when the sumset A + A contains exactly 3k 3 integers. Besides some familiar structures, such a set A can have a configuration composed of “additively minimal triangles.