{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:43:05Z","timestamp":1787323385513,"version":"build-2736575974"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>Let d be a fixed integer, and let W be any d-dimensional linear subspace of $\\mathbb{R}^n$. There then exists a subset I of the n coordinates $\\{1,2,\\dots,n\\}$ of $\\mathbb{R}^n$ of cardinality at least $(\\frac{1}{2}-o(1))n$ such that for every vector $w=(w_1,\\dots,w_n)\\in W$ we have $\\sum_{i\\in I}|w_i|\\leq\\sum_{i\\notin I}|w_i|$. Equivalently, let P be any multiset of n arbitrary vectors in $\\mathbb{R}^d$. Then there exists a subset S of P of size at least $(\\frac{1}{2}-o(1))n$ such that for every vector $u\\in\\mathbb{R}^d$ we have $\\sum_{x\\in S}|\\langle x,u\\rangle|\\leq\\sum_{x\\in P\\setminus S}|\\langle x,u\\rangle|$. A continuous analogue of the former result is also considered.<\/jats:p>","DOI":"10.1137\/090781164","type":"journal-article","created":{"date-parts":[[2010,8,10]],"date-time":"2010-08-10T18:07:59Z","timestamp":1281463679000},"page":"910-920","source":"Crossref","is-referenced-by-count":2,"title":["Dominating Subsets under Projections"],"prefix":"10.1137","volume":"24","author":[{"given":"Rom","family":"Pinchasi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Allan","family":"Pinkus","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,8,10]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02123006"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"B. Chazelle,\n                      The Discrepancy Method: Randomness and Complexity\n                      , Cambridge University Press, Cambridge, UK, 2000.","DOI":"10.1017\/CBO9780511626371"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1963.10500830"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574066"},{"key":"R5","unstructured":"J. Matousek,\n                      Geometric Discrepancy: An Illustrated Guide\n                      , Algorithms Combin. 18, Springer-Verlag, Berlin, 1999."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1976-0425470-0"},{"key":"R7","unstructured":"A. Pinkus,\n                      On $L^1$-Approximation\n                      , Cambridge Tracts in Math. 93, Cambridge University Press, Cambridge, UK, 1989."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1985-0784009-0"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090781164","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:59:23Z","timestamp":1787320763000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090781164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090781164"],"URL":"https:\/\/doi.org\/10.1137\/090781164","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}