Comments for Matt Baker's Math Blog
https://mattbaker.blog
Thoughts on number theory, graphs, dynamical systems, tropical geometry, pedagogy, puzzles, and the p-adics
Sat, 08 Dec 2018 16:10:47 +0000
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Comment on The Balanced Centrifuge Problem by Matt Baker
https://mattbaker.blog/2018/06/25/the-balanced-centrifuge-problem/comment-page-1/#comment-2696
Sat, 08 Dec 2018 16:10:47 +0000http://mattbaker.blog/?p=3805#comment-2696Nice story, thanks for sharing!
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Comment on The Balanced Centrifuge Problem by Pierre Guihéneuf
https://mattbaker.blog/2018/06/25/the-balanced-centrifuge-problem/comment-page-1/#comment-2694
Sat, 08 Dec 2018 11:23:21 +0000http://mattbaker.blog/?p=3805#comment-2694There is another parallel story about this problem.
I felt into it when I was a master’s student, when at some point I had to study determinants of circulant matrices modulo k. I rapidly realized that this problem can be linked to the one about barycenter on roots of unity. I only needed to solve the prime number case, which can be solved directly in the matrix world (or equivalently, as you say, by irreducibility of cyclotomic polynomials), but I found the problem quite funny and proposed it for the international tournament of young mathematicians: it appeared as problem n°5 in the 2012 edition: https://docs.google.com/viewer?a=v&pid=sites&srcid=aXR5bS5vcmd8d3d3fGd4OjJlYmQwNDlkNGFhNzliZDA
I wasn’t aware of the fact that this problem had already been solved at this time. I felt on your blog post only by chance, so glad to know about it!
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Comment on The Balanced Centrifuge Problem by zdu863
https://mattbaker.blog/2018/06/25/the-balanced-centrifuge-problem/comment-page-1/#comment-2671
Mon, 03 Dec 2018 20:23:45 +0000http://mattbaker.blog/?p=3805#comment-2671Same!
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Comment on The Balanced Centrifuge Problem by Maciej
https://mattbaker.blog/2018/06/25/the-balanced-centrifuge-problem/comment-page-1/#comment-2669
Mon, 03 Dec 2018 13:21:58 +0000http://mattbaker.blog/?p=3805#comment-2669Interesting article. I got here through a video that was made about this problem on YouTube. https://www.youtube.com/watch?v=7DHE8RnsCQ8
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Comment on Newton polygons and Galois groups by mabud
https://mattbaker.blog/2014/05/02/newton-polygons-and-galois-groups/comment-page-1/#comment-2587
Tue, 20 Nov 2018 08:11:01 +0000http://mattbakerblog.wordpress.com/?p=612#comment-2587very nice post
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Comment on Effective Chabauty by Naser Talebizadeh Sardari, Hecke eigenvalues, and Chabauty in the deformation space | Quomodocumque
https://mattbaker.blog/2014/04/11/effective-chabauty/comment-page-1/#comment-2524
Mon, 22 Oct 2018 04:02:35 +0000http://mattbakerblog.wordpress.com/?p=580#comment-2524[…] indeed! In the last ten years we’ve seen a huge amount of work refining Chabauty; Matt Baker discusses some of it on his blog, and then there’s the whole nonabelian Chabauty direction launched by Minhyong Kim and pushed […]
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Comment on Riemann-Roch for Graphs and Applications by altenalson
https://mattbaker.blog/2013/10/18/riemann-roch-for-graphs-and-applications/comment-page-1/#comment-2427
Tue, 11 Sep 2018 07:34:26 +0000http://mattbakerblog.wordpress.com/?p=112#comment-2427Hum, that’s unfortunate … Anyway, thanks for your answers and further documentation. I might try the “simulation” solution, but that looks like a very complexe solution to a mundane problem.
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Comment on Riemann-Roch for Graphs and Applications by Matt Baker
https://mattbaker.blog/2013/10/18/riemann-roch-for-graphs-and-applications/comment-page-1/#comment-2425
Mon, 10 Sep 2018 19:44:37 +0000http://mattbakerblog.wordpress.com/?p=112#comment-2425Yes that’s the paper with Norine I was talking about. I think the short answer to your question is that no, there is not a simple way to compute a “score” for the game in advance. The simplest thing, if you want to know in advance what kind of target score to give, might be to run a simulation using only borrowing moves (or only lending moves) and use that as a benchmark.
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Comment on Riemann-Roch for Graphs and Applications by altenalson
https://mattbaker.blog/2013/10/18/riemann-roch-for-graphs-and-applications/comment-page-1/#comment-2423
Mon, 10 Sep 2018 15:49:44 +0000http://mattbakerblog.wordpress.com/?p=112#comment-2423Your expository is nice, but sadly don’t answer this. Do you talk about https://arxiv.org/pdf/math/0608360.pdf ?
I’ll take a look, but honestly I’m not a math heavy person, is there a definitive answer ? Like others, I’m here because of the Numberphile episode. I was hoping to code a nice game around this concept and was wondering if I can compute a score.

Thanks

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Comment on Riemann-Roch for Graphs and Applications by Matt Baker
https://mattbaker.blog/2013/10/18/riemann-roch-for-graphs-and-applications/comment-page-1/#comment-2422
Mon, 10 Sep 2018 14:39:42 +0000http://mattbakerblog.wordpress.com/?p=112#comment-2422Correct, you can also always win with only lending moves. If you use a combination of borrowing and lending moves, I believe it’s an open problem to find describe an optimal strategy for the dollar game, or to find good bounds for the least number of moves required to win the game. But if you use only borrowing (or only lending) moves, more is known; see the references in my paper with Norine and in https://arxiv.org/abs/1107.1313
(You might also enjoy taking a look at my expository paper https://people.math.gatech.edu/~mbaker/pdf/g4g9.pdf)
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