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Nov
11
comment A question about a specific partition of a graph
I'm confused: doesn't $|S|=2$ here, since it contains the pairs $(u,x)$ and $(v,y)$?
Nov
10
comment Can one make Erdős's Ramsey lower bound explicit?
I somehow feel that Erdõs's idea is so fundamental and so generally applicable that the word "trick" doesn't do it justice.
Nov
9
comment What are some very important papers published in non-top journals?
If a paper is published in Math. Ann. when it could have waltzed into Annals, Acta or JAMS, then it counts as an example for my purposes.
Nov
7
comment What are some very important papers published in non-top journals?
Thanks for this. I agree that it is the most likely explanation. And I'm also with the big-list tag, which I had forgotten about, having not posted a question for quite a long time.
Nov
7
comment Almost commuting unitary matrices
Can I check that you are talking about the same question? Here the assumption is not that any two of the matrices approximately commute, but rather the stronger assumption that any two of the matrices can be approximated by a pair of commuting matrices. I can't seem to track down a counterexample to this in the literature.
Nov
6
comment What are some very important papers published in non-top journals?
Agreed -- I think it is an excellent example, though I'd guess that it isn't an example that was "missed" by a top journal -- more that the authors probably (and correctly) didn't think that where they submitted it to would make any difference to the prestige they got from the paper.
Nov
6
comment What are some very important papers published in non-top journals?
I'm not too fussed about the lower limit -- it was meant as a rough guideline.
Nov
6
comment What are some very important papers published in non-top journals?
Let's go for a paper published since 1995. And to avoid having to devise an absolute scale, I'll ask merely that the journal should be lower ranking than one would have expected, given the great importance of the paper.
Oct
6
comment Additive combinatorics and a Diophantine equation
You should be able to get something by combining a number of known results. After the BSG theorem you can apply a lemma of Ruzsa, which allows you to think of your sequence (or rather a suitable subsequence) as living inside a cyclic group that is not much bigger. Then there are results about long arithmetic progressions in sumsets. These will not necessarily be of the form (w,2w,3w,...) but I think a careful look at the proofs should give you this. See for example this paper: arxiv.org/pdf/1103.6000.pdf
Oct
1
comment Proposals for polymath projects
This looks like a great question, and I agree that it would be good for a polymath project. Can I quickly check whether the rank you are talking about is over the reals? (I guess so, or you would have made it a 01 matrix.)
Apr
17
comment A variant of Goldbach Conjecture
Sorry, that wasn't what I meant to ask. I asked the question I actually wanted to ask in a comment on Harald's answer above, which he has now answered. (The question was whether one could do it for all N and not just sufficiently large N.)
Apr
16
comment A variant of Goldbach Conjecture
Can your work can be adapted to prove the result for every $N$ when $p_1,p_2$ and $p_3$ are required to be less than $N$?
Apr
15
comment A variant of Goldbach Conjecture
You mean the result where you insist that $p_1$, $p_2$ and $p_3$ are less than $N$?
Jul
8
comment Nonexistence of an approximately distance-preserving map between discrete cubes
You're right about projection on to the first $n-1$ coordinates. Actually, the case that I'm really interested in is $n/2$ dimensions. In an hour or so I'll modify the question accordingly.
Jun
22
comment Are there very strongly pseudorandom permutations?
I think I've now found a construction that does what I want.
Jun
20
comment Are there any good websites for hosting discussions of mathematical papers?
I think you can make contributions by registering directly with the site, and anybody can read it. But Google Plus is a particularly convenient way of contributing, since all you have to do is write a normal post and add the #spnetwork hashtag. In due course other social networks will be added, but Google Plus has the advantage that public posts are genuinely public.
Jun
20
comment Are there very strongly pseudorandom permutations?
Actually, scratch that -- I miscalculated the information-theoretic bound, which gives that exponentially many would be needed.
Jun
19
comment Are there very strongly pseudorandom permutations?
I now think it may be possible to do something by composing polynomially many Feistel permutations.
Jun
19
comment Are there very strongly pseudorandom permutations?
Yes. I was vague about it, but the precise requirement I would like is that $k$ should be at most a polynomial function of $n$ (or perhaps a very slightly superpolynomial function).
Jun
18
comment Are there very strongly pseudorandom permutations?
Good point -- thanks for the tip.