bio  website  mit.edu/~shopkins 

location  Cambridge, MA  
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1d

revised 
Functions representable as a sum of two permutations of Z/nZ
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1d

answered  Functions representable as a sum of two permutations of Z/nZ 
Nov 30 
comment 
Dyck paths on rectangles
In the time since this question has been asked, there has been a huge amount of interest in "rational Catalan combinatorics." Googling that phrase will give you relevant information; for instance, the slides math.miami.edu/~armstrong/Talks/RCCinDC.pdf and math.umn.edu/~reiner/Talks/AIM2012/AIMIntro.pdf. 
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 24 
comment 
Name for class of flattening permutations
Do you have a bijection between $X_{2n}$ and perfect matchings on $[2n]$? 
Nov 16 
comment 
What is known about multiplayer poker with flop?
It's a little unclear to me what the exact setup 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 reraising forever (or raising arbitrarily high) could be correct. 
Nov 13 
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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 AbelHurwitztype identity
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Nov 4 
answered  Bijective proof of an AbelHurwitztype 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 
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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 
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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/whatistheamplituhedron 
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 
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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 $2^{n2}$ stable states, while for $S_n$ we have $n1$ stable states. So $P_n$ has more states to terminate into. However, the (worstcase) 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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