On Freiman's 3k − 4 Theorem

Mario Huicochea
2019 Uniform Distribution Theory  
AbstractLet X and Y be nonempty finite subsets of 𝕑 and X +Y its sumset. The structures of X and Y when r(X, Y ):= |X +Y |−|X|−|Y | is small have been widely studied; in particular the Generalized Freiman's 3k − 4 Theorem describes X and Y when r(X, Y ) ≤ min{|X|, |Y |} − 4. However, not too much is known about X and Y when r(X, Y ) > min{|X|, |Y |} − 4. In this paper we study the structure of X and Y for arbitrary r(X, Y ).
doi:10.2478/udt-2019-0013 fatcat:23lozhtzyndf5m7e2tbfjskj4u