Structure in sets with logarithmic doubling
Classical Analysis and ODEs
2018-11-05 v2 Combinatorics
Abstract
Suppose that G is an abelian group, A is a finite subset of G with |A+A|< K|A| and eta in (0,1] is a parameter. Our main result is that there is a set L such that |A cap Span(L)| > K^{-O_eta(1)}|A| and |L| = O(K^eta log |A|). We include an application of this result to a generalisation of the Roth-Meshulam theorem due to Liu and Spencer.
Cite
@article{arxiv.1002.1552,
title = {Structure in sets with logarithmic doubling},
author = {Tom Sanders},
journal= {arXiv preprint arXiv:1002.1552},
year = {2018}
}
Comments
13 pp. Slightly refined the proof of Theorem 1.3. Replaced finite fields of characteristic 3 with arbitrary finite fields. Update references. Corrected typos