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bio website mit.edu/~shopkins
location Cambridge, MA
age 24
visits member for 2 years, 11 months
seen 12 mins ago

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/…
Jun
5
comment The space of polynomials with all real roots
But the roots may no longer be real...
May
28
accepted Does the Tutte polynomial of iterated cone graphs detect isomorphism?
May
27
comment Does the Tutte polynomial of iterated cone graphs detect isomorphism?
What does a spanning subgraph mean? I guess it is a subset of the edges that includes at least one edge adjacent to every vertex?
May
27
comment A family of posets
Right, sorry, it is significantly different: skeletal posets only allow taking disjoint unions of posets of the same rank. Meanwhile, I think they are also not a subset of the class here because you are allowed to add multiple greatest or least elements at the same time as well.
May
27
comment A family of posets
This family is very close to the notion of "skeletal poset" in arxiv.org/abs/1402.6178.
May
27
asked Does the Tutte polynomial of iterated cone graphs detect isomorphism?
May
24
comment The most number of points that realize only $k$ distinct distances
@JosephO'Rourke: Have you looked into the many recent techniques and approaches developed to attack the asymptotics of this problem? For instance it is still probably worthwhile to convert this to an incidence question.
May
24
comment The most number of points that realize only $k$ distinct distances
Is this not a very well-known problem?: en.wikipedia.org/wiki/Erd%C5%91s_distinct_distances_problem
May
24
comment Counting Problems where Labeled is Known but Unlabeled is Not
Although in general I guess you are right in that labeled objects are more amenable than unlabeled ones, I think there are some counterexamples to this general behavior: for instance, it is 'easier' to count unlabeled semiorders as opposed to labeled ones (see en.wikipedia.org/wiki/Semiorder#Other_results).
May
22
comment How did Cole factor $2^{67}-1$ in 1903
Wikipedia (en.m.wikipedia.org/wiki/Frank_Nelson_Cole) suggests Cole factored this number in 1903 (or perhaps 1900-1903), if that makes any difference in terms of tools available at the time...
May
15
answered Important open problems that have already been reduced to a finite but infeasible amount of computation