bio  website  jamespropp.org 

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visits  member for  4 years, 7 months 
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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 angledoubling 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 angledoubling 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 cycledecompositions $(25)(46)$, $(13)(27)$, 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 notveryMathOverflowish question "Can someone explain to me what Kirillov and Berenstein are doing in their construction of the $s_i$'s?" 
Aug 26 
comment 
An angledoubling 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 angledoubling trick of Kirillov and Berenstein
Made it clearer that K&B claim what I say they claimed 
Aug 26 
asked  An angledoubling 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 