Summary
We show that if a set B of positive integers has positive upper density, then its difference set D(B) has extremally 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.
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© 1997 Springer-Verlag Berlin Heidelberg
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Bergelson, V., Erdös, P., Hindman, N., Łuczak, T. (1997). Dense Difference Sets and their Combinatorial Structure. In: Graham, R.L., Nešetřil, J. (eds) The Mathematics of Paul Erdös I. Algorithms and Combinatorics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60408-9_14
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DOI: https://doi.org/10.1007/978-3-642-60408-9_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64394-1
Online ISBN: 978-3-642-60408-9
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