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Aug
26
comment Toda Flow Embeddings
@DavidSpeyer: I believe one assumes that $a_i,b_i>0$ and so the Toda flow then preserves positivity. I've added this detail, thank you! I've also added the 4-d toda flow picture.
Aug
26
revised Toda Flow Embeddings
added 111 characters in body
Aug
24
comment open problems in Numerical Analysis
This question is very broad. It would be much better to at least specify a subfield. There's differential equations, linear algebra, fourier analysis, polynomial root finding, etc,etc. In all of these areas, usually the fundamental issue is the curse of dimensionality.
Aug
22
comment Toda Flow Embeddings
@ChristianRemling: you're right but for higher dimensions you inevitably have to exit each face, and this is where the difficulty arises. See for example figure 7 of the above reference.
Aug
22
revised Toda Flow Embeddings
added 283 characters in body
Aug
22
asked Toda Flow Embeddings
Aug
21
comment Collatz property implying infinite “fall below” trajectories, is it known?
Correct me if I'm wrong but such "inverse" problems are easy for generating infinite sets of numbers for which the Collatz conjecture is true. Start with 1 and apply the Collatz algorithm backwards, where you are free to choose whether to double or subtract one/divide by three.
Aug
10
awarded  Nice Answer
Aug
10
revised Examples of unexpected mathematical images
added 124 characters in body
Aug
10
comment Examples of unexpected mathematical images
This is amazing! Here's the paper reference ("Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information"). home.ustc.edu.cn/~zhanghan/cs/Candes%20et%20al.06.pdf
Aug
10
revised Examples of unexpected mathematical images
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Aug
9
revised Examples of unexpected mathematical images
added 428 characters in body
Aug
9
answered Examples of unexpected mathematical images
Jul
31
answered Diagonalization via the Toda flow
Jul
25
revised Quantities whose generating functions are symmetric
added 211 characters in body
Jul
25
revised Quantities whose generating functions are symmetric
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Jul
25
revised Quantities whose generating functions are symmetric
added 143 characters in body
Jul
25
answered Quantities whose generating functions are symmetric
Jul
25
comment Quantities whose generating functions are symmetric
Mahonian statistics for permutations and their generalizations usually enjoy symmetric generating functions. However, you can usually prove these facts via bijections as well. Are you interested then in questions where symmetry is only known to come from a generating function argument?
Jul
17
awarded  Notable Question