bio  website  mit.edu/~shopkins 

location  Cambridge, MA  
age  24  
visits  member for  3 years 
seen  6 hours ago  
stats  profile views  1,228 
1d

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".) 
2d

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 24 
comment 
How can we account for the independent discoveries of place value all using the same direction?
This question would probably be a better fit for: hsm.stackexchange.com. 
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? 
Jun 17 
comment 
What is the definition of plethysm in the representation theory of permutation groups
Example A2.9 in EC2 is a good example, imo. 
Jun 17 
comment 
What is the definition of plethysm in the representation theory of permutation groups
For the symmetric group, the representation theoretic significance of plethysm is related to wreath products. See Theorem A2.8 of Stanley's Enumerative Combinatorics, Vol 2. (By the way, plethysm has a different representationtheoretic significance for the general linear group; and that one is probably a bit easier to understand it is composition of characters). 
Jun 15 
comment 
Counting vertexpermutations of a finite tree which rip all edges
I'm a bit confused by that last comment. Surely linearity of expectation shows that the mean number of nonripped edges is the same for all trees on $n$ vertices, right? 
Jun 15 
comment 
Counting vertexpermutations of a finite tree which rip all edges
Presumably it is also very easy to give a formula for these when $T$ is a star. 
Jun 14 
comment 
Open problems in hyperplane/subspace arrangements?
It's possible that some (new) open problems on hyperplane arrangements will be available later this year at: wwwmath.mit.edu/~rstan/217 
Jun 10 
comment 
Determinantal formulae for Tutte polynomial
The wikipedia page (en.wikipedia.org/wiki/Tutte_polynomial#Gaussian_elimination) seems to make the rather vague assertion that all evaluations for which the Tutte polynomial is computable in polynomial time are actually determinants or Pfaffians. 
Jun 5 
comment 
The space of polynomials with all real roots
Ah I understand now. (By the way, you want to say that u and v are nonpositive vectors.) 
Jun 5 
comment 
The space of polynomials with all real roots
See for instance the comments to the referenced question: mathoverflow.net/questions/207971/… 