bio  website  mit.edu/~darij/www 

location  Karlsruhe (home), Munich (until summer 2011), Cambridge/MA (2011)  
age  26  
visits  member for  5 years, 3 months 
seen  4 hours ago  
stats  profile views  12,090 
I'm just here for asking stupid questions.
2d

revised 
Why does this antisymmetric product factor out a determinant?
added 3 characters in body 
Mar 14 
revised 
Rees algebra isomorphism
added 1 character in body 
Mar 14 
comment 
Rees algebra isomorphism
... isomorphic. Dropping the $t^k$, this means proving that $I^k / \left(J \cap I^k\right) \cong \overline{I}^k$. But the latter is clear, since $\overline{I}^k = \overline{I^k}$ (the projection of $I^k$ onto $\overline{R}$). Once you have these isomorphisms for all $k$, you can take their direct sum and see that it is an algebra isomorphism (easy, because they are very explicit). So the answer to the first question is "Yes". Similarly for the second question. 
Mar 14 
comment 
Rees algebra isomorphism
Correct me if I am wrong, but I believe there are obvious isomorphisms obtained by just considering the different algebras degree by degree (since everything is graded). For instance, for $k \in \mathbb{N}$, the $k$th homogeneous component of $R\left[It\right] / \left(JR\left[t\right] \cap R\left[It\right]\right)$ is $I^k t^k / \left(Jt^k \cap I^k t^k\right)$, while the $k$th homogeneous component of $\overline{R}/\overline{I}$ (where $\overline{R} = R/J$, and where $\overline{I}$ is the projection of $I$ onto $\overline{R}$) is $\overline{I}^k t^k$. It remains to show that these are ... 
Mar 14 
comment 
Dynamics of RSK
Oh! So this wasn't a case of "turning around an octahedron" after all? On the upside, that question perfectly fits the upcoming conference. 
Mar 12 
comment 
Dynamics of RSK
Notice that the composition $\operatorname{revrectsum} \circ \operatorname{diagsum}$ has a simple description: It is the inverse of the map sending a matrix $\left(x_{i,j}\right)_{i,j}$ to $\left(\sum\limits_{k=1}^{i1} x_{k,j} + \sum\limits_{k=1}^{j1} x_{i,k} + x_{i,j}\right)_{i,j}$ (now I am back to using your tropical notations). So it can be called "cohook sum". 
Mar 12 
comment 
Dynamics of RSK
OK, it does not look like double evacuation, because it does not act on the two halves of the matrix separately (at least not on the right two halves). But generally it appears to me that $\operatorname{RSK} \circ \operatorname{revrectsum} \circ \operatorname{diagsum}$ is the simpler map. For example, it maps $\left(\begin{matrix} x & y \\ z & w \end{matrix}\right)$ to $\left(\begin{matrix} \frac{y+z}{x} & y \\ z & \frac{w}{y+z} \end{matrix}\right)$ (in the birational setting; to go tropical, replace $+$ by $\min$ and $/$ by $$). 
Mar 12 
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Dynamics of RSK
Very nice! Do you have an idea if this (or, rather, the conjugate version $\operatorname{RSK} \circ \operatorname{revrectsum} \circ \operatorname{diagsum}$) could be a (double) evacuation map in disguise? 
Mar 12 
comment 
What's the analogue of a Young symmetrizer in the Brauer algebra?
A few years ago I have asked Arun Ram a similar question (I was looking for a lift to the partition algebra, not the Brauer algebra), and he referred me to one of his oldest papers (this is what he said). It might be Arun Ram and Hans Wenzl, Matrix Units for Centralizer Algebras ( sciencedirect.com/science/article/pii/002186939290109Y ). I did not, unfortunately, dig into this; I am not sure if the paper actually settles the question (it seems to be more about generalizing seminormal units). 
Mar 11 
comment 
Fixed space of the square of a symmetric matrix over $\mathbb{F}_2$
What if $M$ is alternating? 
Mar 11 
awarded  linearalgebra 
Mar 11 
answered  Traces and projectors 
Mar 11 
comment 
Traces and projectors
$V$ is $2$dimensional with basis $\left(e,f\right)$. The projectors are projecting on $\mathbb C e$ and $\mathbb C f$, each with kernel $e+f$. The map $T$ projects on $\mathbb C \left(e+f\right)$. This is a counterexample, right? 
Mar 9 
reviewed  No Action Needed What is $K_2(\mathbb{Z}[x,x^{1}])$? 
Mar 4 
comment 
Communal problem books
@MoritzFirsching: These are "Books of abstracts" and "Guest books" in English. None of them seems to be a place for exchanging problems. 
Mar 4 
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Communal problem books
@MoritzFirsching: Where exactly? I cannot find them in there (though they might just be tagged under the wrong tag). 
Mar 3 
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Communal problem books
Oberwolfach still has its book. I don't know if (parts of) it has ever been published, though I suspect most successful solutions have. 
Mar 3 
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Publication in proceedings
@AlexDegtyarev: Because proceedings volumes are usually hard to get (libraries don't always have them, and publishers don't normally put them on the web even behind paywalls), and most of the time, people come to conferences with talks which announce a result that is to be polished and published later. That is different in computer science, but I was talking about mathematics here. 
Mar 3 
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Publication in proceedings
When I see a proceedings paper, I check if there is a journal paper elaborating on it. If not, I start wondering whether it has been disproven before it could get published... 
Feb 28 
comment 
Flooding a cycle digraph via chipfiring: $n^{k1} + n^{k2} + \cdots + 1$ bound (a Norway 199899 problem generalized)
This is an even better proof. Thanks a lot! 