Geodesic
Discrepancy of sums of three arithmetic progressions
The electronic journal of combinatorics, Tome 13 (2006)
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The set system of all arithmetic progressions on $[n]$ is known to have a discrepancy of order $n^{1/4}$. We investigate the discrepancy for the set system ${\cal S}_n^3$ formed by all sums of three arithmetic progressions on $[n]$ and show that the discrepancy of ${\cal S}_n^3$ is bounded below by $\Omega(n^{1/2})$. Thus ${\cal S}_n^3$ is one of the few explicit examples of systems with polynomially many sets and a discrepancy this high.
DOI : 10.37236/1031
Classification : 11K38, 11B75
Mots-clés : discrepancy, arithmetic progression, circulant matrix 
@article{10_37236_1031,
     author = {Ale\v{s} P\v{r}{\'\i}v\v{e}tiv\'y},
     title = {Discrepancy of sums of three arithmetic progressions},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1031},
     zbl = {1109.11039},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1031/}
}
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Aleš Přívětivý. Discrepancy of sums of three arithmetic progressions. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1031

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