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Mathematics professor at Cambridge
Oct
18 |
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Is this Ramsey-type problem an open problem?
@Gerhard Paseman It's not just like an chromatic number problem -- it is asking whether the chromatic number of a certain graph is infinite. (Of course, you must be aware of this or you wouldn't have posted your comment.) Unfortunately, that reformulation doesn't seem to help much, essentially because the graph is too concrete for general facts about graph colouring to be of any use. However, I did once attend a talk that discussed the problem in those terms. |
Aug
3 |
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More on Lebesgue non-measurability
Sigh -- I should have thought harder about the question before posting it. But thanks for the answer. |
Aug
3 |
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Lebesgue non measurability in the plane
See Pietro Majer's comment below. I think it deals with your objection. |
Jul
20 |
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Method for variable substitution in multiple summation
I think you need to be clearer about what the substitution should achieve. Otherwise, the question is a bit too vague. In your examples, I don't see any great simplification resulting from the substitutions, which is what confuses me. |
Jul
18 |
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Examples of non-abelian groups arising in nature without any natural action
That's the group of affine transformations of the rationals: (i,p) sends x to px+i, so (i,p)*(j,q) sends x to p(qx+j)+i=pqx + i+pj. |
Jul
15 |
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Lower bounding the maximum size of sets in a set family with union promise
So s depends on $\epsilon$ and the sets $C_1,\dots,C_k$? |
Jul
14 |
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Current status of Waring-Goldbach problem
Sorry, I take that back -- I was thinking of the result with zeros. But I think the zeros are needed for congruence reasons and it's not clear that one couldn't use some trick. E.g. if k=6 then each kth power is 1 mod 7, except that we can throw in a few $p_i=7$s to deal with that. |
Jul
14 |
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Current status of Waring-Goldbach problem
I'm pretty sure this is known for all k but I'm afraid I don't know a reference. |
Jul
14 |
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Lower bounding the maximum size of sets in a set family with union promise
With your use of the words "given" and "let" I find it hard to work out exactly how the quantification works in your question. Would it be possible to ask it in a more formal way? |
Jul
13 |
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a Ramsey-type question
Yes it was then. |
Jul
13 |
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a Ramsey-type question
By the way, I find this cluster of related questions you are asking very appealing. (My attention was first drawn to them by Noga Alon.) |
Jul
13 |
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a Ramsey-type question
Oops, I meant category. The rough idea I had in mind was that if you cover the $n$-sphere with $m$ open sets, then it would be nice to show that one of them was non-trivial in some topological sense. The trouble is, they're all contractible, but perhaps one could hope that one of them intersected with minus itself is not contractible when considered as a subset of projective $n$-space. That's not quite the same as Lusternik-Schnirelman category but it seems to be in a similar ball park and I don't rule out some way of getting from one to the other. |
Jul
12 |
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a Ramsey-type question
What's known about the continuous version? That is, if you cover the sphere $S_n$ with m closed sets, what can be said about the structures that must be contained in at least one of the sets? If m=n+1 then we get two antipodal points, but what if m=1000? It seems that one ought to get much more. At the moment I don't even see a counterexample to the assertion that if m=n then you get a path from a point to the antipodal point, though that seems a bit optimistic. Am I asking about the Lusternik-Schnirelmann capacity of projective space or something like that? |
Jul
11 |
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What is the complexity of this problem?
Thank you for that interesting answer. In my comment on Dick Lipton's blog I stressed more the importance of the fact that I was looking at a fixed Cayley graph because without that the problem felt much more likely to be NP-complete. But it's nice to have pointers to actual results of that kind. |
Jul
5 |
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Uniformly Convex spaces
Oh, and it also won't change whether it's reflexive. So the answer to your question as asked is trivially no. Do you mean "isomorphic to a space that is uniformly convex"? |
Jul
5 |
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Uniformly Convex spaces
The question needs reformulating slightly, since you can just add a 2D space that's not even strictly convex and it won't change whether $\ell_1$ is finitely represented. |
Jul
3 |
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Examples of common false beliefs in mathematics
I've just added the missing html to fix the link. |
Jul
1 |
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A limiting product formula for the exponential function
I think the two suggestions above don't quite meet the demands of the question (that you should just expand and look at coefficients of separate powers). |
Jul
1 |
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A limiting product formula for the exponential function
I've been away from my computer all day, but the above is essentially the argument I had in mind ... |
Jul
1 |
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Generalizing a problem to make it easier
I have assuredly found an admirable and wholly elementary proof, but this comment box is too narrow to contain it ... |