On The Hereditary Discrepancy of Homogeneous Arithmetic Progressions
Combinatorics
2015-04-10 v2 Number Theory
Abstract
We show that the hereditary discrepancy of homogeneous arithmetic progressions is lower bounded by . This bound is tight up to the constant in the exponent. Our lower bound goes via proving an exponential lower bound on the discrepancy of set systems of subcubes of the boolean cube .
Keywords
Cite
@article{arxiv.1309.6034,
title = {On The Hereditary Discrepancy of Homogeneous Arithmetic Progressions},
author = {Aleksandar Nikolov and Kunal Talwar},
journal= {arXiv preprint arXiv:1309.6034},
year = {2015}
}
Comments
To appear in the Proceedings of the American Mathematical Society