1,276 reputation
1625
bio website mit.edu/~shopkins
location Cambridge, MA
age 24
visits member for 3 years
seen 6 hours ago

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 representation-theoretic 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 vertex-permutations 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 non-ripped edges is the same for all trees on $n$ vertices, right?
Jun
15
comment Counting vertex-permutations 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: www-math.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/…