Published March 11, 2015
| Submitted + Published
Journal Article
Open
Distinct Volume Subsets
Abstract
Suppose that a and d are positive integers with a ≥ 2. Let h_(a,d)(n) be the largest integer t such that any set of n points in ℝ^d contains a subset of t points for which all the nonzero volumes of the [equaton; see abstract in PDF for details] subsets of order a are distinct. Beginning with Erdős in 1957, the function h_(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_(2,d)(n) and show that h_(a,d)(n) is at least a power of n for all a and d.
Additional Information
© 2015 Society for Industrial and Applied Mathematics. Received by the editors January 27, 2014; accepted for publication (in revised form) December 16, 2014; published electronically March 11, 2015. Conlon's research was supported by a Royal Society University Research Fellowship. Fox's research was supported by a Packard Fellowship, by a Simons Fellowship, by NSF grant DMS-1069197, by an Alfred P. Sloan Research Fellowship, and by an MIT NEC Corporation Award. The authors would like to thank Tucker Bane, Andrew Lohr, Jared Marx-Kuo, Joe Mileti, Jessica Shi, Srinivas Vasudevan, and Yufei Zhao for helpful discussions.Attached Files
Published - 140954519.pdf
Submitted - 1401.6734.pdf
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Additional details
- Eprint ID
- 97815
- Resolver ID
- CaltechAUTHORS:20190812-162958151
- Royal Society
- David and Lucile Packard Foundation
- Simons Foundation
- DMS-1069197
- NSF
- Alfred P. Sloan Foundation
- MIT NEC Corporation
- Created
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2019-08-15Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field