Article
On Freiman’s 3K − 4 Theorem
Authors
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 ).
Keywords
Freiman’s 3k − 4 Theorem, sumset, Lev-Smeliansky Theorem.
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
M. Huicochea, “On freiman’s 3K − 4 theorem,” Uniform Distribution Theory, vol. 14, no. 2, pp. 43–68, 2019, doi: 10.2478/udt-2019-0013.
Huicochea M. On freiman’s 3K − 4 theorem. Uniform Distribution Theory. 2019;14(2):43–68. doi:10.2478/udt-2019-0013.
Huicochea, M. (2019), ‘On freiman’s 3K − 4 theorem’, Uniform Distribution Theory, 14(2), pp. 43–68. Available at: https://doi.org/10.2478/udt-2019-0013.
Huicochea, Mario. “On Freiman’s 3K − 4 Theorem.” Uniform Distribution Theory, vol. 14, no. 2, 2019, pp. 43–68. https://doi.org/10.2478/udt-2019-0013.
Huicochea, Mario. “On Freiman’s 3K − 4 Theorem.” Uniform Distribution Theory 14, no. 2 (2019): 43–68. https://doi.org/10.2478/udt-2019-0013.
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Published by: Engineering Journals
