Intereting Posts

Alternatives to show that $|\mathbb{R}|>|\mathbb{Z}|$
Lindenbaum algebra is a free algebra
Picard group and cohomology
What is A Set Raised to the 0 Power? (In Relation to the Definition of a Nullary Operation)
Why do we care about dual spaces?
Why is “the set of all sets” a paradox?
Ramanujan's 'well known' integral, $\int_\frac{-\pi}{2}^\frac{\pi}{2} (\cos x)^m e^{in x}dx$.
Prove $' = \cos x$ without using $\lim\limits_{x\to 0}\frac{\sin x}{x} = 1$
Are there any good algebraic geometry books to recommend?
Determining k: $\int_{6}^{16} \frac{dx}{\sqrt{x^3 + 7x^2 + 8x – 16}} = \frac{\pi}{k}$
Generators for $S_n$
Does a smooth “transition function” with bounded derivatives exist?
A closed subset of an algebraic group which contains $e$ and is closed under taking products is a subgroup of $G$
Convex set of derivatives implies mean value theorem
Is it possible to draw this picture without lifting the pen?

I realize a similar question has been asked before but what I want to know is a little different and is not answered by the link in the answer to that question. I am interested in knowing the best known general upper and lower bounds (non-asymptotic) for an arbitrary Ramsey number $R(k,l)$. Similarly the best known general upper and lower bounds for an arbitrary diagonal Ramsey number $R(k,k)$. It would be good if someone could also tell me asymptotic bounds in these cases as well.(I am not sure whether wikipedia is upto date.)

Thanks.

- Partitioning Integers into Equal Sets to Guarantee Arithmetic Progression
- Girth and monochromatic copy of trees
- Coloring a Complete Graph in Three Colors, Proving that there is a Complete Subgraph
- Ramsey Number R(4,4)
- Good way to learn Ramsey Theory
- Known bounds and values for Ramsey Numbers

- Hilbert's Original Proof of the Nullstellensatz
- probability textbooks
- Literature suggestions: Stochastic Integration; for intuition; for non-mathematicians.
- Learning Complex Geometry - Textbook Recommendation Request
- All real numbers in $$ can be represented as $\sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \dots}}}$
- Prerequisite for Petersen's Riemannian Geometry
- Are there (known) bounds to the following arithmetic / number-theoretic expression?
- What are the applications of functional analysis?
- Is this really an open problem? Maximizing angle between $n$ vectors
- Why define norm in $L_p$ in that way?

I suggest you take a look at this paper by Radziszowski. This site is also up to date with new results about $R(k,l)$.

- Why is there no function with a nonempty domain and an empty range?
- Continuous extensions of continuous functions on dense subspaces
- Graph Proof by induction.
- On Tarski-Knaster theorem
- How to show that $H \cap Z(G) \neq \{e\}$ when $H$ is a normal subgroup of $G$ with $\lvert H\rvert>1$
- Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$
- Why is $\sqrt{-x}*\sqrt{-x}=-x?$
- Homology of $\mathbb{R}^3 – S^1$
- Riemann's Integrals Question
- How to derive this interesting identity for $\log(\sin(x))$
- Integer solutions for $x^3+2=y^2$?
- Maximal inequality for a sequence of partial sums of independent random variables
- Prove that $1 + \frac{1}{2} + \frac{1}{3} + … + \frac{1}{n}$ is not an integer
- How does a complex power series behave on the boundary of the disc of convergence?
- Every space is “almost” Baire?