719 reputation
1319
bio website mit.edu/~shopkins
location Cambridge, MA
age 22
visits member for 1 year, 9 months
seen 39 mins ago

Apr
10
asked Bases of a matroid such that their complement is an independent set
Apr
2
comment Placing numbers $1,2,\ldots,n^3$ in a cube so that numbers of any two adjacent unit subcube are coprime
Is it obvious that the problem gets harder as the dimension increases?
Mar
19
comment Is there a natural notion of completion of a Coxeter system?
Ah right, but I should point out that this is only meaningful when the set $S$ of generators itself is infinite, as in the case of $W = S_{\infty}$.
Mar
19
comment Is there a natural notion of completion of a Coxeter system?
@NathanReading: yes, $\hat{W}$ is generated by products of generators of $W$, but these products are allowed to be infinite (if all terms pairwise commute). This infinite product does not belong to $W$ already (but it does make sense in $GL(E)$).
Mar
18
answered Is there a natural notion of completion of a Coxeter system?
Mar
13
comment Analogues of P vs. NP in the history of mathematics
Perhaps similar to the manifold example I gave earlier, we have the question of whether all smooth manifolds homeomorphic to the standard sphere are diffeomorphic to the standard sphere, answered in the negative by Milnor in 1956 (see en.wikipedia.org/wiki/Exotic_sphere).
Mar
12
awarded  Excavator
Mar
12
revised What are some reasonable-sounding statements that are independent of ZFC?
updated dead link
Mar
10
comment Source for Derogatory Quote About Graph Theory
It was Henry Whitehead, and he said slums not scum. See e.g. the first sentence in arxiv.org/pdf/1111.4050.pdf.
Mar
9
awarded  Autobiographer
Mar
6
comment Is there a natural notion of completion of a Coxeter system?
Allen: Oh but I guess the group you suggest (uniform bound on how far elements can move) may still be the correct setting. Jim: thanks for the reference. I am not sure if simply-laced is important or not.
Mar
5
awarded  Nice Question
Mar
5
comment Is there a natural notion of completion of a Coxeter system?
@AllenKnutson: see edit above.
Mar
5
revised Is there a natural notion of completion of a Coxeter system?
added 1740 characters in body
Mar
5
comment Is there a natural notion of completion of a Coxeter system?
@WillSawin: I don't understand your question. Certainly these (affine/hyperbolic Coxeter groups) are included as possibilities for $(W,S)$. My question is: how do you complete them?
Mar
5
asked Is there a natural notion of completion of a Coxeter system?
Feb
28
answered Why is the right permutohedron order (aka weak order) on $S_n$ a lattice?
Feb
24
answered Definition of infinite permutations
Feb
19
comment Tensor product of hyperplane arrangements
Is it not the case that the intersection lattice of $A_1 \otimes A_2$ is the product of the lattices for $A_1$ and $A_2$?
Feb
16
awarded  Popular Question