Abstract
We investigate a restriction of Paul Erdős’ 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.
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We would like to thank an anonymous referee for suggestions that helped to improve the presentation.
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Hochberg, R., Phillips, P. Discrepancy One among Homogeneous Arithmetic Progressions. Graphs and Combinatorics 32, 2443–2460 (2016). https://doi.org/10.1007/s00373-016-1734-7
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DOI: https://doi.org/10.1007/s00373-016-1734-7