1,286 reputation
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bio website mit.edu/~shopkins
location Cambridge, MA
age 24
visits member for 3 years, 1 month
seen 55 mins ago

Aug
27
comment Finding combinatorial models / statistics
Knowing that it has to be invariant under certain symmetries definitely can help.
Aug
21
comment Three involutions on the set of 6-box Young diagrams
I feel as though the identification of Young diagrams with irreducible representations of the symmetric group is only defined up to the row/column symmetry anyways.
Aug
20
awarded  Nice Answer
Aug
20
comment Important formulas in Combinatorics
@IgorPak: I mean solid partition in the sense used by Wikipedia here: en.wikipedia.org/wiki/Solid_partition.
Aug
19
answered Important formulas in Combinatorics
Aug
18
comment A question about certain sets of permutations of the ordered pairs $(1,1),(1,2),\cdots,(1,n),\cdots,(n,1),(n,2),\cdots,(n,n)$
@BorisBukh: whether you consider the elements of $A_k$ as tuples or permutations is not so important because the question is about the cardinality of the $A_k$.
Aug
18
comment A question about certain sets of permutations of the ordered pairs $(1,1),(1,2),\cdots,(1,n),\cdots,(n,1),(n,2),\cdots,(n,n)$
It is extremely confusing to use $S_n$ to denote a set whose members are being permuted rather than the symmetric group on $n$ letters.
Aug
12
comment Pattern Avoidance in Poset Permutations
The article mentioned above is published here: link.springer.com/article/10.1007/s11083-015-9367-7.
Aug
6
comment Intuition behind if neither $D$ nor $K-D$ are equivalent to an effective divisor, then $\deg(D) = g-1$?
If you want intuition about this statement, you should be precise about what you are taking as your definition of genus.
Aug
2
comment Terminology in combinatorics
Sorry, I was confused by the use of "common". (I thought it meant "encompassing both of the properties" rather than "usual".)
Jul
31
comment Why is it so hard to prove Toeplitz' conjecture?
The problem is deceptively hard because a "Jordan curve" can be very badly behaved and look quite different from what intuitively one might think of as a "closed curve."
Jul
31
asked Pattern Avoidance in Poset Permutations
Jul
27
comment A question on representation of graphs
@DavidSpeyer: maybe you could come up with a more evocative title for this question?
Jul
25
comment Survey papers on the role played by PDE in mathematics
"...the fact that this PDE result also gives the Poincaré conjecture and the more general geometrisation conjecture makes it (again in my opinion) the best piece of mathematics we have seen in the last ten years. It is truly a landmark achievement for the entire discipline." - from arxiv.org/abs/math/0610903
Jul
22
comment Incidence geometry and matrices
The question might be better phrased without the word "minimum." Clearly if for each $A$ there is some $d$ so that this is achievable, then there is a minimum $d$ for fixed $m$ and $n$ because there are only finitely many such $A$. The question is whether for each $A$ there is some $d$.
Jul
10
awarded  Yearling
Jul
7
comment Are there any Algebraic Geometry Theorems that were proved using Combinatorics?
In the same spirit as my last comment, but (as I am told) now establishing a new result, here is a link to a tropical proof of the maximal rank conjecture for quadrics: arxiv.org/abs/1505.05460
Jul
5
comment Which journals publish research announcements?
Isn't it important not just that the proofs are formally correct and vouched for, but that they are presented in a coherent manner so that a motivated reader can actually understand what you have done?
Jul
4
comment Idea of using etale site
"a cohomology theory for varieties with coefficients in a field of characteristic zero" - Do you mean to say in a field of positive characteristic?
Jun
22
comment Details on the Symmetric Group action on chambers of the Shi Arrangement
Can you explain in more detail how you want $S_{n+1}$ to act on the chambers of the Shi arrangement?