{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T11:41:12Z","timestamp":1693482072592},"reference-count":5,"publisher":"Wiley","issue":"3-4","license":[{"start":{"date-parts":[[2002,9,19]],"date-time":"2002-09-19T00:00:00Z","timestamp":1032393600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2002,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let \u212c\ufe01<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-1.gif\" xlink:title=\"urn:x-wiley:10429832:media:RSA10055:tex2gif-stack-1\" \/> denote the family which consists of all subsets <jats:italic>S<\/jats:italic><jats:sub>1<\/jats:sub> \u00d7 \u2026 \u00d7 <jats:italic>S<jats:sub>d<\/jats:sub><\/jats:italic>, where <jats:italic>S<jats:sub>i<\/jats:sub><\/jats:italic> \u2286 [<jats:italic>n<\/jats:italic>], and <jats:italic>S<jats:sub>i<\/jats:sub><\/jats:italic> \u2260 \u2205\ufe01, for <jats:italic>i<\/jats:italic> = 1, \u2026 , <jats:italic>d<\/jats:italic>. We compute the <jats:italic>L<\/jats:italic><jats:sub>2<\/jats:sub>\u2010discrepancy of \u212c\ufe01<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-2.gif\" xlink:title=\"urn:x-wiley:10429832:media:RSA10055:tex2gif-stack-2\" \/> and give estimates for the <jats:italic>L<jats:sub>p<\/jats:sub><\/jats:italic>\u2010discrepancy of \u212c\ufe01<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-3.gif\" xlink:title=\"urn:x-wiley:10429832:media:RSA10055:tex2gif-stack-3\" \/> for 1 \u2264 <jats:italic>p<\/jats:italic> \u2264 \u221e.\u00a9 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 205\u2013215, 2002<\/jats:p>","DOI":"10.1002\/rsa.10055","type":"journal-article","created":{"date-parts":[[2002,10,21]],"date-time":"2002-10-21T13:37:09Z","timestamp":1035207429000},"page":"205-215","source":"Crossref","is-referenced-by-count":3,"title":["On the discrepancy of combinatorial rectangles"],"prefix":"10.1002","volume":"21","author":[{"given":"Noga","family":"Alon","sequence":"first","affiliation":[]},{"given":"Benjamin","family":"Doerr","sequence":"additional","affiliation":[]},{"given":"Tomasz","family":"\u0141uczak","sequence":"additional","affiliation":[]},{"given":"Tomasz","family":"Schoen","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2002,9,19]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00180-1"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/0471722154"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0425-1"},{"key":"e_1_2_1_5_2","first-page":"101","article-title":"On the best constant in the Khinchin\u2010Kahane inequality","volume":"109","author":"Lata\u0142a R.","year":"1994","journal-title":"Stud Math"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","first-page":"197","DOI":"10.4064\/sm-58-2-197-208","article-title":"On the best constants in the Khinchin Inequality","volume":"58","author":"Szarek S. J.","year":"1976","journal-title":"Stud Math"}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.10055","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.10055","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T13:16:26Z","timestamp":1693401386000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.10055"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9,19]]},"references-count":5,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2002,10]]}},"alternative-id":["10.1002\/rsa.10055"],"URL":"https:\/\/doi.org\/10.1002\/rsa.10055","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9,19]]}}}