On the discrepancy of combinatorial rectangles

Authors:
Noga Alon;Benjamin Doerr;Tomasz Łuczak;Tomasz Schoen
Affiliations:
Schools of Mathematics and Computer Science, Raymond and Beverly Sackler, Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel;Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Strasse 4, 24098 Kiel, Germany;Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Strasse 4, 24098 Kiel, Germany;Department of Discrete Mathematics, Adam Mickiewicz University, 60-769 Poznan, Poland
Venue:
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Year:
2002

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Note: On the L2-discrepancy

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Abstract

Let Bdn denote the family which consists of all subsets S1 ×... × Sd, where Si ⊆ [n], and Si ≠ Φ for i = 1,..... d. We compute the L2-discrepancy of Bdn and give estimates for the Lp-discrepancy of Bdn for 1 ≤ p ≤ ∞.