On Freiman’s 3k − 4 Theorem

Mario Huicochea

doi:10.2478/udt-2019-0013

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On Freiman’s 3k − 4 Theorem

Uniform distribution theory

Volume 14 (2019): Issue 2 (December 2019)

By: Mario Huicochea

Open Access

|Mar 2020

Abstract

Let 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 ).

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Articles in this issue

DOI: https://doi.org/10.2478/udt-2019-0013 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 43 - 68

Submitted on: Apr 19, 2018

Accepted on: May 27, 2019

Published on: Mar 27, 2020

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Freiman’s 3k − 4 Theorem,

sumset,

Lev-Smeliansky Theorem

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2020 Mario Huicochea, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 14 (2019): Issue 2 (December 2019)