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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 14. Issue 2


Published on

December, 2019


Pages

43-68


DOI

https://doi.org/10.2478/udt-2019-0013

Article

On Freiman’s 3k − 4 Theorem


Authors

Mario Huicochea


Abstract

Let X and Y be nonempty finite subsets of ℤ 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 ).


Citation

Huicochea, M. (2019). On Freiman’s 3k − 4 Theorem. Uniform distribution theory, 14(2), 43-68. https://doi.org/10.2478/udt-2019-0013