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Is there a good online reference that lists known bounds on Ramsey numbers (and is relatively up to date)? The wikipedia page only has numbers for $R_2(n,m)$.

I am specifically interested in known bounds and values for hypergraph Ramsey Numbers, i.e. 2 colorings of k-subsets (or 2 colorings of the edges of a complete k-uniform hypergraph). These are commonly denoted $R_k(m,n)$. A shallow internet search has yielded only a couple sets of papers and notes on bounds.

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I wanted to add the tag Ramsey theory or numbers, but neither exists. Should we add these tags or would they be unnecessary? –  AnonymousCoward Dec 12 '10 at 7:09

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up vote 9 down vote accepted

The best resource online is the (frequently updated) survey Small Ramsey Numbers by Stanisław Radziszowski, in The Electronic Journal of Combinatorics. Go to http://www.combinatorics.org/ and click on the link for "dynamic surveys". When I first wrote this answer (December 12, 2010), the survey version dated August 2009. As of this edit (June 8, 2014), the most recent update on the Ramsey numbers paper is dated January 12, 2014. The paper gives extensive references where one can find complete proofs or details of the computations involved.

Radziszowski himself is responsible for several improvements to the bounds listed there, and you may want to check his page for recent results not yet included. Although the emphasis of the paper is on exact values, it also includes references for asymptotics and general upper bounds. With respect to the latter, there have been significant recent advances (particularly, by Conlon and his collaborators), and you may want to check the pages of the authors listed on page 9 of the survey, for possible improvements.

I found through another answer in this site a link to Geoffrey Exoo's page (somewhat under construction, it seems), which contains additional improvements due to Exoo (mostly unpublished).

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Ah, yes I had found the paper by Conlon et. al. on the arxiv and it contained several of the results that I wanted, but it was also missing some. Thank you this is what I was looking for precisely! –  AnonymousCoward Dec 12 '10 at 7:13

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