Comments for Shadows of Simplicity
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Just some math notes.
Thu, 09 Aug 2018 19:41:53 +0000
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Comment on Compositional Inverse Pairs, the Inviscid Burgers-Hopf Equation, and the Stasheff Associahedra by Tom Copeland
https://tcjpn.wordpress.com/2014/09/17/compositional-inverse-pairs-the-inviscid-burgers-hopf-equation-and-the-stasheff-associahedra/#comment-441
Thu, 09 Aug 2018 19:41:53 +0000http://tcjpn.wordpress.com/?p=484#comment-441Related: “An Introduction to Wave Equations and Solitons” by Richard S. Palais https://www.ma.utexas.edu/users/uhlen/solitons/notes.pdf and the later post here on “The Lie Triad … .”
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Comment on The Elliptic Lie Triad: KdV and Riccati Equations, Infinigens, and Elliptic Genera by Tom Copeland
https://tcjpn.wordpress.com/2015/10/12/the-elliptic-lie-triad-kdv-and-ricattt-equations-infinigens-and-elliptic-genera/#comment-440
Thu, 09 Aug 2018 19:36:20 +0000http://tcjpn.wordpress.com/?p=4223#comment-440Related: “An Introduction to Wave Equations and Solitons” by Richard S. Palais https://www.ma.utexas.edu/users/uhlen/solitons/notes.pdf
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Comment on Lagrange à la Lah by Pre-Lie algebras, Cayley’s analytic trees, and mathemagical forests | Shadows of Simplicity
https://tcjpn.wordpress.com/2011/04/11/lagrange-a-la-lah/#comment-425
Tue, 10 Jul 2018 21:40:47 +0000http://tcjpn.wordpress.com/?p=23#comment-425[…] the action of the resulting operator at each vertex on of the immediate lower vertex (see also Lagrange a la Lah). For example, if three leaves are attached by edges, or branches, directly to a lower vertex, the […]
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Comment on Mathemagical Forests by Pre-Lie algebras, Cayley’s analytic trees, and mathemagical forests | Shadows of Simplicity
https://tcjpn.wordpress.com/2008/06/12/mathemagical-forests/#comment-424
Tue, 10 Jul 2018 21:40:45 +0000http://tcjpn.wordpress.com/2008/06/12/mathemagical-forests#comment-424[…] see the relation to Cayley’s work of 1857 as described in my pdf Mathemagical Forests (MF), let the generators be represented by the vectors (infinitesimal Lie generators) and where , […]
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Comment on Bernoulli Appells by Tom Copeland
https://tcjpn.wordpress.com/2014/12/10/appells-for-the-bernoullis/#comment-423
Mon, 09 Jul 2018 18:13:28 +0000http://tcjpn.wordpress.com/?p=698#comment-423Cf. also https://golem.ph.utexas.edu/category/2008/02/metric_spaces.html
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Comment on An Intriguing Tapestry: Number triangles, polytopes, Grassmannians, and scattering amplitudes by Tom Copeland
https://tcjpn.wordpress.com/2016/11/20/an-intriguing-tapestry-number-triangles-polytopes-grassmannians-and-scattering-amplitudes/#comment-422
Wed, 27 Jun 2018 22:09:52 +0000http://tcjpn.wordpress.com/?p=5696#comment-422Other early refs: “Motivic Amplitudes and Cluster Coordinates” by John Golden, Alexander B. Goncharov, Marcus Spradlin, Cristian Vergu, Anastasia Volovich https://arxiv.org/abs/1305.1617 and https://fqxi.org/community/forum/topic/2361. Another recent talk by He is “Scattering Forms from Geometries at Infinity” https://indico.ipmu.jp/indico/event/145/contributions/2231/attachments/1886/2248/talk_IPMUSong_He.pdf
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Comment on An Intriguing Tapestry: Number triangles, polytopes, Grassmannians, and scattering amplitudes by Tom Copeland
https://tcjpn.wordpress.com/2016/11/20/an-intriguing-tapestry-number-triangles-polytopes-grassmannians-and-scattering-amplitudes/#comment-421
Mon, 25 Jun 2018 20:50:20 +0000http://tcjpn.wordpress.com/?p=5696#comment-421On the Eulerians, see “Scattering Equations: Real Solutions and Particles on a Line” by Freddy Cachazo, Sebastian Mizera, Guojun Zhang. https://arxiv.org/abs/1609.00008
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Comment on An Intriguing Tapestry: Number triangles, polytopes, Grassmannians, and scattering amplitudes by Tom Copeland
https://tcjpn.wordpress.com/2016/11/20/an-intriguing-tapestry-number-triangles-polytopes-grassmannians-and-scattering-amplitudes/#comment-420
Mon, 25 Jun 2018 14:19:41 +0000http://tcjpn.wordpress.com/?p=5696#comment-420See the modified Mathoverflow question for more references: https://mathoverflow.net/questions/182622/an-intriguing-tapestry-number-triangles-polytopes-grassmannians-and-scatteri. (Now 10 upvotes and seven downvotes.)
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Comment on An Intriguing Tapestry: Number triangles, polytopes, Grassmannians, and scattering amplitudes by Tom Copeland
https://tcjpn.wordpress.com/2016/11/20/an-intriguing-tapestry-number-triangles-polytopes-grassmannians-and-scattering-amplitudes/#comment-419
Sun, 24 Jun 2018 18:46:30 +0000http://tcjpn.wordpress.com/?p=5696#comment-419From 4gravitons (https://4gravitons.wordpress.com/2017/07/20/more-travel/) remarking on talks at the Amplitudes 2017 conference: Between the two of them, Nima and Yuntao covered an interesting development, tying the Amplituhedron together with the string theory-esque picture of scattering amplitudes pioneered by Freddy Cachazo, Song He, and Ellis Ye Yuan (or CHY). There’s a simpler (and older) Amplituhedron-like object called the associahedron that can be thought of as what the Amplituhedron looks like on the surface of a string, and CHY’s setup can be thought of as a sophisticated map that takes this object and turns it into the Amplituhedron.
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Comment on An Intriguing Tapestry: Number triangles, polytopes, Grassmannians, and scattering amplitudes by Tom Copeland
https://tcjpn.wordpress.com/2016/11/20/an-intriguing-tapestry-number-triangles-polytopes-grassmannians-and-scattering-amplitudes/#comment-418
Sun, 24 Jun 2018 18:03:43 +0000http://tcjpn.wordpress.com/?p=5696#comment-418More recent related references in https://oeis.org/A019538, https://oeis.org/A049019, and https://oeis.org/A133437
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