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visits member for 4 years, 7 months
seen 3 hours ago

I am interested in combinatorics, probability, dynamical systems, and various other topics.


6h
comment $L^2$ discrepancy bound for sequences in $[0,1)$
Sorry my first comment was misleading. What I meant to say was that for the van der Corput sequence, the behavior of $D_n$ appears to be $n^{1/2}$ (albeit with lots of fluctuations), and I suspect that this is best possible, in the sense that for any $c<1/2$, $D_n / n^c$ is unbounded, regardless of what sequence $x_1,x_2,...$ one is looking at.
18h
comment $L^2$ discrepancy bound for sequences in $[0,1)$
I think (based on preliminary experiments) that typical behavior of $D_n$ is on the order of $n^{1/2}$.
18h
asked $L^2$ discrepancy bound for sequences in $[0,1)$
1d
awarded  Popular Question
Aug
29
awarded  Popular Question
Aug
27
comment An angle-doubling trick of Kirillov and Berenstein
I reluctantly second Stefan's proposal. (Is closing a thread something the original poster can do? Or is someone with moderation powers needed?)
Aug
27
comment An angle-doubling trick of Kirillov and Berenstein
It seems that (as Darij speculated) Kirillov and Berenstein didn't do what I said they did; their arguments use other properties of the $t_i$'s. To see this, let $t_1$, $t_2$, and $t_3$ be the permutations of $\{1,2,\dots,7\}$ with respective cycle-decompositions $(25)(46)$, $(13)(27)$, and $(26)(45)$. Then the $t_i$'s satisfy the hypotheses of my claim but the $s_i$'s don't satisfy the conclusions of my claim. This leaves me with only the not-very-MathOverflow-ish question "Can someone explain to me what Kirillov and Berenstein are doing in their construction of the $s_i$'s?"
Aug
26
comment An angle-doubling trick of Kirillov and Berenstein
It is indeed possible that K&B's proof of the Theorem 1.1 makes use of properties of the $t_i$'s that I haven't included. (This would account for why I haven't been able to prove $(s_3 s_4)^3 = 1$ using just the Coxeter relations.) I don't understand the article well enough to assess this. So I guess I should have started the original post by saying "It seems to me that Kirillov and Berenstein..."
Aug
26
revised An angle-doubling trick of Kirillov and Berenstein
Made it clearer that K&B claim what I say they claimed
Aug
26
asked An angle-doubling trick of Kirillov and Berenstein
Aug
8
awarded  Nice Question
Jul
2
awarded  Inquisitive
Jul
2
awarded  Curious
Jun
25
awarded  Nice Question
Jun
16
revised Postnikov's approach to perfect matchings of graphs
deleted 1 character in body
Jun
16
accepted Postnikov's approach to perfect matchings of graphs
Jun
13
answered Postnikov's approach to perfect matchings of graphs
Jun
12
accepted Two to the power of a triangular number: bijections
Jun
11
awarded  Nice Question
Jun
11
answered Two to the power of a triangular number: bijections