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bio website mit.edu/~shopkins
location Cambridge, MA
age 23
visits member for 2 years, 4 months
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Nov
25
comment A funny factorization of the Jacobian coming from the lines on the Fermat cubic
$X$ is a cubic surface in $\mathbb{P}^3$.
Nov
25
comment Massive cancellations
I guess you mean to conjecture that $A$ is tame when it consists of algebraic numbers?
Nov
16
comment What is known about multiplayer poker with flop?
It's a little unclear to me what the exact set-up is. You make it sound like players can raise the bet, but in this case it seems like you need to assume players have fixed chip stacks or else re-raising forever (or raising arbitrarily high) could be correct.
Nov
13
comment Combinatorial Databases
I'm not sure that it is exactly what you're looking for, but findstat.org is another nice combinatorial database.
Nov
6
accepted Combinatorial proof of the Cauchy identity for double Schubert polynomials
Nov
5
asked Combinatorial proof of the Cauchy identity for double Schubert polynomials
Nov
4
revised Bijective proof of an Abel-Hurwitz-type identity
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Nov
4
answered Bijective proof of an Abel-Hurwitz-type identity
Nov
1
comment The formula for a perhaps basic identity (move from stackexchange)
This question seems related too: mathoverflow.net/questions/123926/…
Oct
27
comment System of boolean equations, Satisfiability
You should make it clearer that you are not trying to solve this system (which may be inconsistent), but rather satisfy as many (in some sense) of the equations as possible.
Oct
5
comment An Intriguing Tapestry: Number triangles, polytopes, Grassmannians, and scattering amplitudes
Well, the definitive source explaining the combinatorics behind the positive Grassmannian is of course arxiv.org/abs/math/0609764.
Oct
5
comment An Intriguing Tapestry: Number triangles, polytopes, Grassmannians, and scattering amplitudes
It seems that there are already some very similar questions on MO: mathoverflow.net/questions/142841/… mathoverflow.net/questions/143339/what-is-the-amplituhedron
Aug
18
comment Notion of infinity in categories
I think the OP is asking about what conditions on a category we can impose to force the transitivity property to hold, not what conditions on objects we can impose.
Aug
16
comment Duration and critical groups order in sandpile models and chip firing games
@FelixGoldberg: that's true. But keep in mind there is the subtle distinction between configurations (distributions of sand on the nonsink vertices) and divisors (distributions of sand on all the vertices). So above I am wrong to say the stable divisors form a monoid; it is the stable configurations which do.
Aug
16
revised Duration and critical groups order in sandpile models and chip firing games
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Aug
16
comment Duration and critical groups order in sandpile models and chip firing games
Note that this example also runs exactly opposite to the intuition mentioned by the OP: for $P_n$ we have $2^{n-2}$ stable states, while for $S_n$ we have $n-1$ stable states. So $P_n$ has more states to terminate into. However, the (worst-case) stopping time is much longer for $P_n$ than $S_n$.
Aug
16
revised Duration and critical groups order in sandpile models and chip firing games
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Aug
16
revised Duration and critical groups order in sandpile models and chip firing games
deleted 599 characters in body
Aug
15
comment Embed one Coxeter System into another
@DavidSpeyer: I think that manuscript of Stembridge only addresses embeddings of crystollagraphic root systems in simply-laced ones, in which case there is an easy way to see the embedding via "folding" which arises from the fixed-point set of an automorphism of the Coxeter graph. But the embeddings discussed by the OP (of $H_3$ into $D_6$ or $H_4$ into $E_8$) are different and more complicated than this.
Aug
15
comment Duration and critical groups order in sandpile models and chip firing games
By the way, as to the OP's intuition that a larger sandpile group gives "more opportunities to terminate": what is really at issue with such an intuition is not the sandpile group (whose elements are the recurrent configurations) but rather the monoid of stable divisors because we play the game until we reach a state that is stable. The size of this monoid is just the product of all the degrees of the vertices in $G$.