bio  website  mit.edu/~darij/www 

location  Karlsruhe (home), Munich (until summer 2011), Cambridge/MA (2011)  
age  25  
visits  member for  4 years, 10 months 
seen  10 hours ago  
stats  profile views  11,321 
I'm just here for asking stupid questions.
2d

comment 
Obscure Names in Mathematics
Speaking of tropical geometry: the Aztec diamond and the arctic circle theorem ( en.wikipedia.org/wiki/Aztec_diamond ). 
Oct 15 
comment 
Isotypic components of the action of the symmetric group on polynomials
"it is a regular representation": why? 
Oct 15 
comment 
Isotypic components of the action of the symmetric group on polynomials
I think he wants a decomposition into $S_n$submodules. 
Oct 9 
comment 
Generalized CauchyBinet sum over a fixed subset of indices
Isn't it just the CauchyBinet formula applied to the matrices $A_{[m],[nj]}$ and $B_{[nj],[m]}$ instead of $A$ and $B$ ? 
Oct 9 
comment 
Generalized CauchyBinet sum over a fixed subset of indices
I think the simplest answer will be $\det\left(A_{[m],[nj]} B_{[nj],[m]}\right)$. 
Oct 8 
comment 
Does this permanent have a closed form?
For $n = 2$, the result is a fraction whose numerator is an irreducible degree4 polynomial. If anything factors for higher $n$, then I don't think the factors will be any simpler than this polynomials... 
Oct 8 
comment 
Deligne's exterior power
What do you want to do with two variables? If $\alpha x + \beta y = 0$, then $\alpha x \wedge \beta y = 0$. 
Oct 8 
comment 
Deligne's exterior power
What happens if you replace my $k$ by the polynomial ring $\mathbb{F}_2\left[\alpha,\beta,\gamma\right]$, change the definition of $L$ to $L = M / \left< \alpha x + \beta y + \gamma z, \alpha^2 x, \alpha^2 y, \alpha^2 z, \beta^2 x, \beta^2 y, \beta^2 z, \gamma^2 x, \gamma^2 y, \gamma^2 z \right>$, and change the image of $f$ to $k / \left(\alpha^2, \beta^2, \gamma^2\right)$ ? 
Oct 8 
comment 
Deligne's exterior power
Nice. I tried to simplify the calculation like that, but I failed, so I decided to keep the symmetric form. 
Oct 8 
comment 
NonConvex Polygons with “Antipodal Visibility”
Take a triangle $ABC$ with $\leftAB\right = \leftAC\right$ and with $\measuredangle BAC$ very small (thus an isosceles triangle with an apex very high up). Let $H$ be its orthocenter. I am fairly sure $ABHC$ has antipodal visibility (and is not convex). 
Oct 8 
answered  Deligne's exterior power 
Oct 8 
comment 
Is there a Gröbner basis analogue that exists for vector spaces?
Thank you; I meant "nonlinear" indeed. 
Oct 7 
revised 
Is there a Gröbner basis analogue that exists for vector spaces?
added 1 character in body; edited tags 
Oct 7 
comment 
Is there a Gröbner basis analogue that exists for vector spaces?
V is a subspace of the vector space on which your coordinate system is defined? Then a basis $\left(v_1, v_2, \ldots, v_n\right)$ has the property that you desire if and only if it is a permutation of the list of rows of a matrix in rowechelon form. I am fairly sure that this is wellknown; many people motivate Groebner basis theory as a noncommutative analogue of classical linear algebra (Groebner basis <~~> row echelon form; reduced Groebner basis <~~> reduced row echelon form). 
Oct 2 
comment 
Is there a bijection of permutations onto mathematical objects that preserve information about descents?
The map that sends a permutation to its descent set itself is a very useful thing. It is the map $S_n \to Q_n$ in Loday/Ronco "Hopf Algebra of the Planar Binary Trees" ( sciencedirect.com/science/article/pii/S0001870898917595 ), and factors through $Y_n$ as shown on page 1 of that paper. 
Sep 30 
awarded  Explainer 
Sep 30 
awarded  Nice Question 
Sep 30 
revised 
Antiarithmetic product of symmetric functions: (why) is it integral?
added 247 characters in body 
Sep 29 
asked  Antiarithmetic product of symmetric functions: (why) is it integral? 
Sep 28 
comment 
Which math paper maximizes the ratio (importance)/(length)?
@DanielLitt: Thank you, but I fear you overestimated my progress. I still don't know what a derived category is and don't feel that I have the time and peace of mind to read myself into them properly. 