Published June 2019
| Version Submitted
Journal Article
Open
A construction for difference sets with local properties
Creators
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1.
California Institute of Technology
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2.
Princeton University
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3.
Baruch College
Abstract
We construct finite sets of real numbers that have a small difference set and strong local properties. In particular, we construct a set A of n real numbers such that |A−A| = n^(log_23) and that every subset A′⊆A of size k satisfies |A′−A′| ≥ k^(log_23). This construction leads to the first non-trivial upper bound for the problem of distinct distances with local properties.
Additional Information
© 2019 Elsevier Ltd. Received 20 December 2018, Accepted 24 March 2019, Available online 17 April 2019. This research project was done as part of the 2018 CUNY Combinatorics REU, supported by NSF grant DMS-1710305. Supported by Caltech's Summer Undergraduate Research Fellowships (SURF) program. Supported by NSF grant 1802787. Supported by NSF award DMS-1710305 and PSC-CUNY award 61666-00-49.Attached Files
Submitted - 1812.07651.pdf
Files
1812.07651.pdf
Additional details
Identifiers
- Eprint ID
- 95457
- Resolver ID
- CaltechAUTHORS:20190513-160703905
Related works
- Describes
- https://arxiv.org/abs/1812.07651 (URL)
Funding
- NSF
- DMS-1710305
- Caltech Summer Undergraduate Research Fellowship (SURF)
- NSF
- DMS-1802787
- City University of New York
- 61666-00-49
Dates
- Created
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2019-05-14Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field