Mapping Incidences
Combinatorics
2011-08-16 v2 Number Theory
Abstract
We show that any finite set S in a characteristic zero integral domain can be mapped to the finite field of order p, for infinitely many primes p, preserving all algebraic incidences in S. This can be seen as a generalization of the well-known Freiman isomorphism lemma, and we give several combinatorial applications (such as sum-product estimates).
Keywords
Cite
@article{arxiv.0711.4407,
title = {Mapping Incidences},
author = {Van H. Vu and Melanie Matchett Wood and Philip Matchett Wood},
journal= {arXiv preprint arXiv:0711.4407},
year = {2011}
}
Comments
15 pages, to appear in the Journal of the London Mathematical Society. Section 3 on Erd\H{o}s distance problem from the previous version has been removed, since the most current version of arXiv:math/0301343v3 [math.CO] has the added restriction that -1 is not a square. Other minor revisions were also made