{"id":167709,"date":"2013-01-01T00:00:00","date_gmt":"2013-01-01T00:00:00","guid":{"rendered":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/msr-research-item\/on-the-hereditary-discrepancy-of-homogeneous-arithmetic-progressions\/"},"modified":"2018-10-16T22:12:03","modified_gmt":"2018-10-17T05:12:03","slug":"on-the-hereditary-discrepancy-of-homogeneous-arithmetic-progressions","status":"publish","type":"msr-research-item","link":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/publication\/on-the-hereditary-discrepancy-of-homogeneous-arithmetic-progressions\/","title":{"rendered":"On The Hereditary Discrepancy of Homogeneous Arithmetic Progressions"},"content":{"rendered":"

We show that the hereditary discrepancy of homogeneous arithmetic progressions is lower bounded by n<\/span>1<\/span>\/<\/span><\/span><\/span>O<\/span>(<\/span>log<\/span><\/span>log<\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>. This bound is tight up to the constant in the exponent. Our lower bound goes via proving an exponential lower bound on the discrepancy of set systems of subcubes of the boolean cube {<\/span>0<\/span>,<\/span>1<\/span>}<\/span>d<\/span><\/span><\/span><\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

We show that the hereditary discrepancy of homogeneous arithmetic progressions is lower bounded by n1\/O(loglogn). This bound is tight up to the constant in the exponent. Our lower bound goes via proving an exponential lower bound on the discrepancy of set systems of subcubes of the boolean cube {0,1}d<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Proceedings of the AMS (to appear)","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"Proceedings of the AMS (to 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