# Tagged Questions

1answer
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### Graham-Rothschild via Hales-Jewett

I am currently reading the recent preprint of Dodos, Kanellopoulos, Tyros, where the ambitiously short proof of Density Hales Jewett theorem is provided. The important ingredient is Graham-Rothschild ...
3answers
723 views

### Density Ramsey theorems with explicit asymptotics

I wonder what interesting and non-trivial examples of density Ramsey theorems with explicit asymptotics are there? I'm aware of two examples: Szemerédi's theorem and density Hales-Jewett theorem. ...
3answers
604 views

### Arithmetic progressions of length 3 in subset of Z_n of size n^d

Let $A\subset\mathbb{Z}/n\mathbb{Z}$ such that: $|A|>n^{d}$ ($0< d <1$). Let $C=\{(x,y,2y-x)\in A\times A \times A\}$ be the set of $3$-term arithmetic progressions within $A$. [The ...
3answers
1k views

### Cliques, Paley graphs and quadratic residues

A question I've thought about, on and off for a long time, is how to improve the best bounds that (seem to be) known for the clique numbers of Paley graphs. If p=1 mod 4 is a prime, we can define the ...
1answer
1k views

### Monochromatic triangles in every two-coloring of the plane?

An old problem (possibly due to Erdős and Graham?): given a triangle $T$ and a two-coloring of the plane, does there necessary exist a monochromatic congruent copy of $T$? Here "monochromatic" means ...