Construction of one-dimensional subsets of the reals not containing similar copies of given patterns

By Tamás Keleti. 2008

49 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f9d4f06a862ac588a6c9219e5c33e129cb79413a

How researchers see this paper

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

In Discrete Mathematics and Combinatorics

1. Pablo Shmerkin
2. I. Łaba
3. Vincent Chan
4. M. Pramanik
5. Larry Guth

In Geometry and Topology

1. Pablo Shmerkin
2. I. Łaba
3. Vincent Chan
4. M. Pramanik
5. Meng Wu
6. Michael Hochman

In Mathematical Physics

1. Pablo Shmerkin
2. I. Łaba
3. M. Pramanik
4. Meng Wu
5. P. P. Varj'u
6. Michael Hochman
7. Máté Matolcsi
8. Jonathan M. Fraser

Citations in the corpus

• Salem sets with no arithmetic progressions (2015, background): “Keleti’s constructions are deterministic and it is notoriously difficult to establish that given deterministic sets support measures with any polynomial Fourier decay, let alone maximal decay.”
• Finite configurations in sparse sets (2013, background): “Keleti also proves the existence of sets E ⊂ R with dimH(E) = 1 that avoid all “onedimensional parallelograms” {x, x + y, x + z, x + y + z}, with y, z 6= 0 [20], or all similar copies of any 3-point configuration from a given sequence {(xi, yi, zi)}i=1 [21].”