Mathematics – Number Theory
Scientific paper
2004-03-21
Mathematics
Number Theory
9 pages, minor corrections made
Scientific paper
We study the extent to which sets A in Z/NZ, N prime, resemble sets of integers from the additive point of view (``up to Freiman isomorphism''). We give a direct proof of a result of Freiman, namely that if |A + A| < K|A| and |A| < c(K)N then A is Freiman isomorphic to a set of integers. Because we avoid appealing to Freiman's structure theorem, we get a reasonable bound: we can take c(K) > exp(-cK^2 log K). As a byproduct of our argument we obtain a sharpening of the second author's result on sets with small sumset in torsion groups. For example if A is a subset of F_2^n, and if |A + A| < K|A|, then A is contained in a coset of a subspace of size no more than 2^{CK^2}|A|.
Green Ben
Ruzsa Imre Z.
No associations
LandOfFree
Sets with small sumset and rectification does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Sets with small sumset and rectification, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sets with small sumset and rectification will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-701649