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On Freiman's 3k − 4 Theorem
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