John-type theorems for generalized arithmetic progressions and iterated sumsets
Combinatorics
2008-05-21 v2
Abstract
A classical theorem of Fritz John allows one to describe a convex body, up to constants, as an ellipsoid. In this article we establish similar descriptions for generalized (i.e. multidimensional) arithmetic progressions in terms of proper (i.e. collision-free) generalized arithmetic progressions, in both torsion-free and torsion settings. We also obtain a similar characterization of iterated sumsets in arbitrary abelian groups in terms of progressions, thus strengthening and extending recent results of Szemer\'edi and Vu.
Cite
@article{arxiv.math/0701005,
title = {John-type theorems for generalized arithmetic progressions and iterated sumsets},
author = {Terence Tao and Van Vu},
journal= {arXiv preprint arXiv:math/0701005},
year = {2008}
}
Comments
20 pages, no figures, to appear, Adv. in Math. Some minor changes thanks to referee report