English

Discrepancy One among Homogeneous Arithmetic Progressions

Combinatorics 2018-07-17 v1

Abstract

We investigate a restriction of Paul Erdos' well-known problem from 1936 on the discrepancy of homogeneous arithmetic progressions. We restrict our attention to a finite set S of homogeneous arithmetic progressions, and ask when the discrepancy with respect to this set is exactly 1. We answer this question when S has size four or less, and prove that the problem for general S is NP-hard, even for discrepancy 1.

Keywords

Cite

@article{arxiv.1601.02997,
  title  = {Discrepancy One among Homogeneous Arithmetic Progressions},
  author = {Robert Hochberg and Paul Phillips},
  journal= {arXiv preprint arXiv:1601.02997},
  year   = {2018}
}
R2 v1 2026-06-22T12:28:05.564Z