Summary
We provide a short proof of a recent result of Elkin in which large subsets of \(\{1,\ldots,N\}\) free of three-term progressions are constructed.
To Mel Nathanson
Mathematics Subject Classifications (2010). Primary 11B25, Secondary 11B75
The first author holds a Leverhulme Prize and is grateful to the Leverhulme Trust for their support. This paper was written while the authors were attending the special semester in ergodic theory and additive combinatorics at MSRI.
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F. Behrend. On sets of integers which contain no three terms in arithmetic progression, Proc. Nat. Acad. Sci., 32:331–332, 1946
M. Elkin, An improved construction of progression-free sets, available at http://arxiv.org/abs/0801.4310
R. Graham, On the growth of a van der Waerden-like function, Integers, 6:#A29, 2006
B. Landman, A. Robertson and C. Culver, Some new exact van der Waerden numbers, Integers, 5(2):#A10, 2005
Acknowledgement
The authors are grateful to Tom Sanders for helpful conversations.
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Green, B., Wolf, J. (2010). A Note on Elkin’s Improvement of Behrend’s Construction. In: Chudnovsky, D., Chudnovsky, G. (eds) Additive Number Theory. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68361-4_9
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DOI: https://doi.org/10.1007/978-0-387-68361-4_9
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