On sets of integers not containing long arithmetic progressions
Combinatorics
2007-05-23 v1 Number Theory
Abstract
We construct subsets of {1,...,N} of cardinality at least N exp(-C(log N)^{1/(k+1)}) which do not contain arithmetic progressions of length 2^k+1. This extends a result of Behrend (1946) concerning sets which do not contain aritmetic progressions of length 3.
Cite
@article{arxiv.math/0108155,
title = {On sets of integers not containing long arithmetic progressions},
author = {Izabella Laba and Michael T. Lacey},
journal= {arXiv preprint arXiv:math/0108155},
year = {2007}
}
Comments
8 pages