{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T05:34:39Z","timestamp":1772516079640,"version":"3.50.1"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:p> In this paper, we introduce the notion of [Formula: see text]-centerpoints for any set [Formula: see text] of [Formula: see text] points in [Formula: see text]. These unify and generalize previous results such as the classical centerpoint theorem,<jats:sup>1<\/jats:sup> and the recently-proven ray-shooting theorem.<jats:sup>2<\/jats:sup> We define two variants: affine [Formula: see text]-centerpoints, and topological [Formula: see text]-centerpoints. We prove their equivalence in [Formula: see text], and conjecture that these are in fact equivalent in any dimension. We present the first non-trivial bounds for these problems in [Formula: see text], as well as present several conjectures related to them. <\/jats:p>","DOI":"10.1142\/s0218195915500107","type":"journal-article","created":{"date-parts":[[2015,10,15]],"date-time":"2015-10-15T07:17:40Z","timestamp":1444893460000},"page":"163-185","source":"Crossref","is-referenced-by-count":3,"title":["k-Centerpoints Conjectures for Pointsets in \u211dd"],"prefix":"10.1142","volume":"25","author":[{"given":"Nabil H.","family":"Mustafa","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris-Est, LIGM, Equipe A3SI, ESIEE Paris, France"}]},{"given":"Saurabh","family":"Ray","sequence":"additional","affiliation":[{"name":"Computer Science, NYU, Abu Dhabi, United Arab Emirates"}]},{"given":"Mudassir","family":"Shabbir","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Information Technology University, Lahore, Pakistan"}]}],"member":"219","published-online":{"date-parts":[[2015,10,15]]},"reference":[{"key":"p_1","first-page":"291","volume":"21","author":"Rado R.","year":"1947","journal-title":"J. Lond. Math. Soc."},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1142\/S021819599600023X"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1145\/256292.256294"},{"key":"p_7","first-page":"20","author":"Donoho D. L.","year":"1994","journal-title":"Ann. Stat."},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2007.02.006"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00181519"},{"issue":"10","key":"p_11","volume":"13","author":"Bukh B.","year":"2006","journal-title":"Electron. J. Combinat."},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-008-9124-4"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90115-7"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-010-9263-2"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-010-0073-8"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-012-9419-3"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009502"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195915500107","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T02:39:04Z","timestamp":1565145544000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195915500107"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9]]},"references-count":13,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2015,10,15]]},"published-print":{"date-parts":[[2015,9]]}},"alternative-id":["10.1142\/S0218195915500107"],"URL":"https:\/\/doi.org\/10.1142\/s0218195915500107","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9]]}}}