On a generalisation of Roth's theorem for arithmetic progressions and applications to sum-free subsets
Number Theory
2012-11-15 v2 Combinatorics
Abstract
We prove a generalisation of Roth's theorem for arithmetic progressions to d-configurations, which are sets of the form {n_i+n_j+a}_{1 \leq i \leq j \leq d} where a, n_1,..., n_d are nonnegative integers, using Roth's original density increment strategy and Gowers uniformity norms. Then we use this generalisation to improve a result of Sudakov, Szemer\'edi and Vu about sum-free subsets and prove that any set of n integers contains a sum-free subset of size at least log n (log log log n)^{1/32772 - o(1)}.
Keywords
Cite
@article{arxiv.1210.1729,
title = {On a generalisation of Roth's theorem for arithmetic progressions and applications to sum-free subsets},
author = {Jehanne Dousse},
journal= {arXiv preprint arXiv:1210.1729},
year = {2012}
}
Comments
12 pages