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Arithmetic structures in random sets Hamel, Mariah

Abstract

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.

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Attribution-NonCommercial-NoDerivatives 4.0 International

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