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Apr
5 |
accepted | Orthogonal basis for the multilinear polynomials with zero “trace” |
Apr
5 |
awarded | Revival |
Apr
5 |
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Orthogonal basis for the multilinear polynomials with zero “trace”
Qing Xiang and Rafael Plaza pointed me to this paper. |
Apr
5 |
answered | Orthogonal basis for the multilinear polynomials with zero “trace” |
Apr
1 |
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About expectation norms on graphs
Cross-posted on cs.se: cs.stackexchange.com/questions/40929/…. |
Mar
8 |
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About the small set expansion conjecture
I think cstheory.se would be a better fit for this question. The OP should also reveal their sources – specifically where the statement "one seems to prove" comes from. Meanwhile, let me just comment that a set of measure $\delta$ is what the OP thinks it is. |
Feb
5 |
awarded | Necromancer |
Feb
4 |
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Orthogonal basis for the multilinear polynomials with zero “trace”
@VladimirDotsenko It's available here: cs.toronto.edu/~yuvalf/WimmerFriedgut.pdf. |
Feb
3 |
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Orthogonal basis for the multilinear polynomials with zero “trace”
The conjecture is actually known to be true now. |
Feb
3 |
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Orthogonal basis for the multilinear polynomials with zero “trace”
@VladimirDotsenko They are multilinear in the sense that the square of a variable never appears. It's a summation $\sum$ rather than a product $\prod$. The first few vectors are $x_1-x_2$, $x_1+x_2-2x_3$, $x_1+x_2+x_3-3x_4$, and so on. Looks pretty multilinear to me. Moreover, for given $d$, the basis function is a homogeneous degree $d$ polynomial, so in this example, everything is a (homogeneous) linear polynomial. |
Jul
18 |
awarded | Yearling |
Jul
2 |
awarded | Curious |
May
9 |
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Orthogonal basis for the multilinear polynomials with zero “trace”
@darij I obtained the basis by taking the double cosets corresponding to $\binom{[n]}{k}$, computing Young's orthogonal representation, summing all rows (or all columns), and normalizing to remove all the square roots. I'm not sure that's the same as what you'd get from Young's natural representation, but I didn't check. |
May
8 |
asked | Orthogonal basis for the multilinear polynomials with zero “trace” |
Dec
15 |
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How can an extremely mathematically talented young person be helped to fulfill his/her potential?
I would say that most of history's greatest researchers restricted themselves to one "field" such as physics, chemistry or biology. They might have contributed to more than one area, however. The same can be said about many great mathematicians. Mathematics is vast enough. |
Dec
14 |
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How can an extremely mathematically talented young person be helped to fulfill his/her potential?
I'm not worried about the lack of practical use. Not everything has to be measured against being practical. The practical use of novels and poetry is diminishing (unless you're lucky), though literary skills are invaluable in defending criminals; this is no reason to stop aspiring authors. |
Dec
13 |
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How can an extremely mathematically talented young person be helped to fulfill his/her potential?
What the kid needs is an appreciation of abstraction. Computing the Jordan forms of 100 matrices isn't going to help with that. S/he needs to see some real mathematics, do some problem solving, develop some toy theories. Even do some calculations on paper. It helps develop intuition. |
Dec
13 |
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How can an extremely mathematically talented young person be helped to fulfill his/her potential?
I hope the kid is beyond this level... |
Dec
13 |
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How can an extremely mathematically talented young person be helped to fulfill his/her potential?
Strongly disagree. Being a successful mathematician is a fulfilling life, and it doesn't prevent one from living life to its fullest. |
Oct
30 |
awarded | Popular Question |