dc.contributor.author | Conlon, David | |
dc.contributor.author | Fox, Jacob | |
dc.contributor.author | Gasarch, William | |
dc.contributor.author | Harris, David G. | |
dc.contributor.author | Ulrich, Douglas | |
dc.contributor.author | Zbarsky, Samuel | |
dc.date.accessioned | 2015-06-09T13:02:41Z | |
dc.date.available | 2015-06-09T13:02:41Z | |
dc.date.issued | 2015-03 | |
dc.date.submitted | 2014-12 | |
dc.identifier.issn | 0895-4801 | |
dc.identifier.issn | 1095-7146 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/97231 | |
dc.description.abstract | Suppose that a and d are positive integers with a ≥ 2. Let h[subscript a,d](n) be the largest integer t such that any set of n points in R[superscript d] contains a subset of t points for which all the nonzero volumes of the ([t over a]) subsets of order a are distinct. Beginning with Erdos in 1957, the function h[subscript 2,d](n) has been closely studied and is known to be at least a power of n. We improve the best known bound for h[subscript 2,d](n) and show that h[subscript a,d](n) is at least a power of n for all a and d. | en_US |
dc.description.sponsorship | David & Lucile Packard Foundation (Fellowship) | en_US |
dc.description.sponsorship | Simons Foundation (Fellowship) | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (Grant DMS-1069197) | en_US |
dc.description.sponsorship | Alfred P. Sloan Foundation (Fellowship) | en_US |
dc.description.sponsorship | NEC Corporation (MIT Award) | en_US |
dc.language.iso | en_US | |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1137/140954519 | en_US |
dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
dc.source | Society for Industrial and Applied Mathematics | en_US |
dc.title | Distinct Volume Subsets | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Conlon, David, Jacob Fox, William Gasarch, David G. Harris, Douglas Ulrich, and Samuel Zbarsky. “Distinct Volume Subsets.” SIAM J. Discrete Math. 29, no. 1 (January 2015): 472–480. © 2015 Society for Industrial and Applied Mathematics | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Fox, Jacob | en_US |
dc.relation.journal | SIAM Journal on Discrete Mathematics | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Conlon, David; Fox, Jacob; Gasarch, William; Harris, David G.; Ulrich, Douglas; Zbarsky, Samuel | en_US |
mit.license | PUBLISHER_POLICY | en_US |
mit.metadata.status | Complete | |