Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T14:01:57.974Z Has data issue: false hasContentIssue false
  • English
  • Français

Long arithmetic progressions in sum-sets and the number x-sum-free sets

Published online by Cambridge University Press:  25 February 2005

E. Szemerédi  and
V. H. Vu
E. Szemerédi
Affiliation:
Computer Science Department, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA. E-mail: szemered@cs.rutgers.edu
V. H. Vu
Affiliation:
Department of Mathematics, University of California at San Diego, La Jolla, CA 92093-0112, USA. E-mail: vanvu@ucsd.eduhttp://www.math.ucsd.edu/~vanvu/
Get access

Abstract

In this paper we obtain optimal bounds for the length of the longest arithmetic progression in various kinds of sum-sets. As an application, we derive a sharp estimate for the number of sets $A$ of residues modulo a prime $n$ such that no subsum of $A$ equals $x$ modulo $n$, where $x$ is a fixed residue modulo $n$.

Keywords

long arithmetic progressionsum-setFreiman inverse theoremsum-free set05A1611B2511P32
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 90 , Issue 2 , March 2005 , pp. 273 - 296
Copyright
2005 London Mathematical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)