On the discrepancy of coloring finite sets

D. Hajela

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-3

Abstract:

Given a subset S of { 1 , … , n } and a map X : { 1 , … , n } → { − 1 , 1 } , (i.e. a coloring of { 1 , … , n } with two colors, say red and blue) define the discrepancy of S with respect to X to be d X ( S ) = | ∑ i ∈ S X ( i ) | (the difference between the reds and blues on S ). Given n subsets of { 1 , … , n } , a question of Erdos was to find a coloring of { 1 , … , n } which simultaneously minimized the discrepancy of the n subsets. We give new and simple proofs of some of the results obtained previously on this problem via an inequality for vectors.

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:892638

DOI: 10.1155/S0161171290001168

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