We prove various results in additive combinatorics for subsets of random sets. In particular we extend Sarkozy's theorem and a theorem of Green on long arithmetic progressions in sumsets to dense subsets of random sets with asymptotic density 0. Our proofs require a transference argument due to Green and Green-Tao which enables us to apply known results for sets of positive upper density to subsets of random sets which have positive relative density. We also prove a density result which states that if a subset of a random set has positive relative density, then the sumset of the subset must have positive upper density in the integers. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/2838 |
| Date | 11 1900 |
| Creators | Hamel, Mariah |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Format | 2205235 bytes, application/pdf |
| Rights | Attribution-NonCommercial-NoDerivatives 4.0 International, http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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