Intereting Posts

Probability Brownian motion is positive at two points
Closed-forms of infinite series with factorial in the denominator
Prove that $\mathbb{C} \ncong \mathbb{C}\oplus\mathbb{C}$
some elementary questions about cardinality
Unique weak solution to the biharmonic equation
A proof that powers of two cannot be expressed as the sum of multiple consecutive positive integers that uses binary representations?
Problem about limit of Lebesgue integral over a measurable set
Combinatorial Proof
One more question about decay of Fourier coefficients
On the origins of the (Weierstrass) Tangent half-angle substitution
Prove every element of $G$ has finite order.
Group structure on pointed homotopy classes
For which $s\in\mathbb R$, is $H^s(\mathbb T)$ a Banach algebra?
Relative compactness of metric space
Find the exact value of the infinite sum $\sum_{n=1}^\infty \big\{\mathrm{e}-\big(1+\frac1n\big)^{n}\big\}$

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.

- $K_6$ contains at least two monochromatic $K_3$ graphs.
- Is there only one counter example in $K_5$ for $R(3,3)$?
- K5 Graph Avoidance Coloring Game
- Girth and monochromatic copy of trees
- Chromatic Triangles on a $K_{17}$ graph
- Graham's Number : Why so big?

- Logistic model differential equation
- showing $-\eta(s) = \lim_{z \ \to \ -1} \sum_{n=1}^\infty z^{n} n^{-s}$
- math-biography of mathematicians
- Cancellation problem: $R\not\cong S$ but $R\cong S$ (Danielewski surfaces)
- A sequence of $n^2$ real numbers which contains no monotonic subsequence of more than $n$ terms
- Books in foundations of mathematical logic
- Proving the existence of a proof without actually giving a proof
- Suggestion on good probability theory book
- Category theory text that defines composition backwards?
- Good problem books at a relatively advanced level?

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

- Representation theory of locally compact groups
- How to show that the orbits of the action of Gs on S \ {s} have lengths that are equal in pairs.
- Expected maximum absolute value of $n$ iid standard Gaussians?
- Integral basis of an extension of number fields
- Find remaining vertices of a square, given 2
- Prove: $\sum {{a_{{n_k}}}} < \infty \Rightarrow \sum {|{a_n}| < \infty } $
- Problem Heron of Alexandria.
- Area of Validity of Writing an Exponential Integral as Sum of IntegralSinus and -Cosinus
- Existence of the least common multiple in a Unique Factorization Domain
- Why differentiability implies continuity, but continuity does not imply differentiability?
- Question about notation for Minors / How to determine a set of invariant factors given a relations matrix
- Elements of the form $aX^2 + bY^2$ in a finite field.
- Number of solutions of $x^2_1+\dots+x^2_n=0,$ $x_i\in \Bbb{F}_q.$
- Understanding of extension fields with Kronecker's thorem
- Image of the Veronese Embedding