Distinct Volume Subsets
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,...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2015
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| Online Access: | http://hdl.handle.net/1721.1/97231 |
| _version_ | 1811082304015040512 |
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| author | Conlon, David Fox, Jacob Gasarch, William Harris, David G. Ulrich, Douglas Zbarsky, Samuel |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Conlon, David Fox, Jacob Gasarch, William Harris, David G. Ulrich, Douglas Zbarsky, Samuel |
| author_sort | Conlon, David |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:00:59Z |
| format | Article |
| id | mit-1721.1/97231 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:00:59Z |
| publishDate | 2015 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/972312022-10-01T07:37:42Z Distinct Volume Subsets Conlon, David Fox, Jacob Gasarch, William Harris, David G. Ulrich, Douglas Zbarsky, Samuel Massachusetts Institute of Technology. Department of Mathematics Fox, Jacob 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. David & Lucile Packard Foundation (Fellowship) Simons Foundation (Fellowship) National Science Foundation (U.S.) (Grant DMS-1069197) Alfred P. Sloan Foundation (Fellowship) NEC Corporation (MIT Award) 2015-06-09T13:02:41Z 2015-06-09T13:02:41Z 2015-03 2014-12 Article http://purl.org/eprint/type/JournalArticle 0895-4801 1095-7146 http://hdl.handle.net/1721.1/97231 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 http://dx.doi.org/10.1137/140954519 SIAM Journal on Discrete Mathematics 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. application/pdf Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics |
| spellingShingle | Conlon, David Fox, Jacob Gasarch, William Harris, David G. Ulrich, Douglas Zbarsky, Samuel Distinct Volume Subsets |
| title | Distinct Volume Subsets |
| title_full | Distinct Volume Subsets |
| title_fullStr | Distinct Volume Subsets |
| title_full_unstemmed | Distinct Volume Subsets |
| title_short | Distinct Volume Subsets |
| title_sort | distinct volume subsets |
| url | http://hdl.handle.net/1721.1/97231 |
| work_keys_str_mv | AT conlondavid distinctvolumesubsets AT foxjacob distinctvolumesubsets AT gasarchwilliam distinctvolumesubsets AT harrisdavidg distinctvolumesubsets AT ulrichdouglas distinctvolumesubsets AT zbarskysamuel distinctvolumesubsets |