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The hereditary discrepancy is nearly independent of the number of colors
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Journal Article
The hereditary discrepancy is nearly independent of the number of colors
2004
Overview
We investigate the discrepancy (or balanced coloring) problem for hypergraphs and matrices in arbitrary numbers of colors. We show that the hereditary discrepancy in two different numbers a,b∈N≥2a, b \\in {\\mathbb N} _{\\ge 2} of colors is the same apart from constant factors, i.e., \\[ herdisc(⋅,b)=Θ(herdisc(⋅,a)).\\operatorname {herdisc}(\\cdot ,{b}) = \\Theta ( \\operatorname {herdisc}(\\cdot ,{a})). \\] This contrasts the ordinary discrepancy problem, where no correlation exists in many cases.
Publisher
American Mathematical Society
