We show that if a set B of positive integers has positive upper density, then its difference set D(B) has extremely rich combinatorial structure, both additively and multiplicatively. If on the other hand only the density of D(B) rather than B is assumed to be positive, one is not guaranteed any multiplicative structure at all and is guaranteed only a modest amount of additive structure.
CITATION STYLE
Bergelson, V., Erdős, P., Hindman, N., & Łuczak, T. (2013). Dense difference sets and their combinatorial structure. In The Mathematics of Paul Erdos I, Second Edition (pp. 133–146). Springer New York. https://doi.org/10.1007/978-1-4614-7258-2_10
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