JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (4): 7-10.doi: 10.6040/j.issn.1671-9352.0.2017.220

Previous Articles     Next Articles

On sumsets and translates of vector subspaces over finite fields

CAO Ya-meng, LI Jiao, LI Guo-quan*   

  1. College of Mathematics Science, Tianjin Normal University, Tianjin 300387, China
  • Received:2017-05-10 Online:2018-04-20 Published:2018-04-13

PDF (PC)

472

Abstract: Let F np be a finite field model and A,B⊂F np, it is shown that there exist a vector subspaces V and a constant D>0 such that dim V≥D and A+B contains a translate of the subspace V.

Key words: dual group, sumset, Bohr set

CLC Number: 

  • O157.1
[1] GREEN B. Surveys in Combinatorics 2005[M]. Cambridge: Cambridge University Press, 2005: 1-27.
[2] GREEN B, TAO T. Freimans theorem in finite fields via extremal set theory[J]. Combin Probab Comput, 2009, 18:335-355.
[3] GOWERS W, WOLF J. Linear forms and higher-degree uniformity for functions on F np[J]. Geom Funct Anal, 2011, 21:36-69.
[4] BATEMAN M, KATZ N. New bounds on cap sets[J]. J Amer Math Soc, 2012, 25:585-613.
[5] EVEN-ZOHAR C, LOVETT S. The Freiman-Ruzsa theorem over finite fields[J]. J Combin Theory, 2014, 125:333-341.
[6] WOLF J. Finite field models in arithmetic combinatorics-ten years on[J]. Finite Fields and Their Appl, 2015, 32:233-274.
[7] 李芳, 关爱霞, 李国全. 有限Abel群中的和集与Bohr集的子集[J]. 山东大学学报(理学版), 2017, 52(2):39-43. LI Fang, GUAN Aixia, LI Guoquan. Sumsets and subsets of Bohr sets in finite abelian groups[J]. Journal of Shandong University(Natural Science), 2017, 52(2):39-43.
[8] CROOT E, ŁABA I, SISASK O. Arithmetic progressions in sumsets and Lp-almost-periodicity[J]. Combin Probab Comput, 2013, 22:351-365.
[1] LI Fang, GUANG Ai-xia, LI Guo-quan. Sumsets and subsets of Bohr sets in finite abelian groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 39-43.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd