A Note on Elkin’s Improvement of Behrend’s Construction

By B. Green, Julia Wolf. 2008

86 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f2f0e7c00783374adcf99efbba4a8d0f5fe34702

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Helger Lipmaa
2. Peter Keevash

In Discrete Mathematics and Combinatorics

1. Helger Lipmaa
2. Peter Keevash
3. Matthew Kwan
4. Allan Siu Lun Lo
5. Deryk Osthus
6. D. Kühn
7. Stefan Glock
8. Jie Han

In Geometry and Topology

1. Helger Lipmaa
2. Peter Keevash
3. Jie Han

Citations in the corpus

• Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions. (2020, unknown): “A slight improvement on Behrend’s construction was found by Elkin [11], with an alternative approach by Green and Wolf [15], but this does not change the form of the lower bound in (15).”
• Progression-Free Sets and Sublinear Pairing-Based Non-Interactive Zero-Knowledge Arguments (2012, background): “Our proof is closely based on [13] but it has a sharper constant inside Ω .”
• Surveys in Combinatorics 2011: Hypergraph Turán problems (2011, background): “It would be very interesting to tighten these bounds: this is connected with regularity theory (see Section 10) and bounds for Roth’s theorem (see [90, 166].”