In topological graph theory, the Wilson operations are a group of six transformations on graph embeddings. They are generated by two involutions on embeddings, surface duality and Petrie duality, and have the group structure of the symmetric group on three elements. They are named for Stephen E. Wilson, who published them for regular maps in 1979; they were extended to all cellular graph embeddings (embeddings all of whose faces are topological disks) by . The operations are: identity, duality, Petrie duality, Petrie dual of dual, dual of Petrie dual, and dual of Petrie dual of dual or equivalently Petrie dual of dual of Petrie dual. Together they constitute the group S3. These operations be characterized algebraically as the only outer automorphisms of certain group-theoretic representations of embedded graphs.Via their action on dessins d'enfants, they can be used to study the absolute Galois group of the rational numbers. One can also define corresponding operations on the edges of an embedded graph, the partial dual and partial Petrie dual, such that performing the same operation on all edges simultaneously is equivalent to taking the surface dual or Petrie dual. These operations generate a larger group, the ribbon group, acting on the embedded graphs. As an abstract group, it is isomorphic to , the -fold product of copies of the three-element symmetric group. (Wikipedia).
Woodrow Wilson: A World War and a League of Nations (1913 - 1921)
Woodrow Wilson was president during a time when a lot was changing in the world. World War I broke out, and as hard as he tried to keep America out of it, it was inevitable that it enter the action, only to emerge as the world's premiere superpower. Wilson had a lot of progressive views, a
From playlist American History
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After running on the campaign, "He Kept Us Out of the War," Woodrow Wilson brings the United States into World War I in April 1917. #TheWorldWars Subscribe for more History: http://histv.co/SubscribeHistoryYT Check out exclusive HISTORY videos and full episodes: http://www.history.com/vid
From playlist War & Battle | History
Special Forces by the Numbers | History
Special Forces have played a vital role in every U.S. military conflict since its founding. Find out more about what it takes to become part of this elite group. Newsletter: https://www.history.com/newsletter Website - http://www.history.com /posts Facebook - https://www.facebook.com/Hist
From playlist Examine the Past | History
The Selection: Exit Interviews - Episode 2 | History
Participants who dropped out after Episode 2 explain what prompted them to leave "The Selection". #TheSelection Subscribe for more from The Selection: Special Operations Experiment and other great HISTORY shows: http://histv.co/SubscribeHistoryYT Find out more about the show and watch fu
From playlist The Selection: Special Operations Experiment | Official Series Playlist | History
The Selection: Exit Interviews - Episode 3 | History
Participants who dropped out after Episode 3 explain what prompted them to leave "The Selection". #TheSelection Subscribe for more from The Selection: Special Operations Experiment and other great HISTORY shows: http://histv.co/SubscribeHistoryYT Find out more about the show and watch fu
From playlist The Selection: Special Operations Experiment | Official Series Playlist | History
The Selection: Exit Interviews - Episode 4 | History
Participants who dropped out after Episode 4 explain what prompted them to leave "The Selection". #TheSelection Subscribe for more from The Selection: Special Operations Experiment and other great HISTORY shows: http://histv.co/SubscribeHistoryYT Find out more about the show and watch fu
From playlist The Selection: Special Operations Experiment | Official Series Playlist | History
The Selection: Contestant Bio - Ryan Kent | History
Learn more about "The Selection" contestant Ryan Kent in this web exclusive. #TheSelection Subscribe for more from The Selection: Special Operations Experiment and other great HISTORY shows: http://histv.co/SubscribeHistoryYT Find out more about the show and watch full episodes on our si
From playlist The Selection: Special Operations Experiment | Official Series Playlist | History
The Rise of the Nazis | History
Take a look at key events that led to the Nazi party's rise to power in Germany. Subscribe for more from HISTORY: http://histv.co/SubscribeHistoryYT Newsletter: https://www.history.com/newsletter Website - http://www.history.com Facebook - https://www.facebook.com/History Twitter - https
From playlist Hitler in History
The Selection: Exit Interviews - Episode 6 | History
Participants who dropped out after Episode 6 explain what prompted them to leave "The Selection". #TheSelection Subscribe for more from The Selection: Special Operations Experiment and other great HISTORY shows: http://histv.co/SubscribeHistoryYT Find out more about the show and watch fu
From playlist The Selection: Special Operations Experiment | Official Series Playlist | History
MIT 8.851 Effective Field Theory, Spring 2013 View the complete course: http://ocw.mit.edu/8-851S13 Instructor: Iain Stewart In this lecture, the professor discussed extension to multiple collinear directions, and ultrasoft-collinear factorization via field redefinitions. License: Creati
From playlist MIT 8.851 Effective Field Theory, Spring 2013
MIT 8.851 Effective Field Theory, Spring 2013 View the complete course: http://ocw.mit.edu/8-851S13 Instructor: Iain Stewart In this lecture, the professor discussed hard-collinear factorization, quark and gluon building blocks for operators, loops and IR divergences, and 0-bin. License
From playlist MIT 8.851 Effective Field Theory, Spring 2013
Vortices and Generalised Symmetry by Mathew Bullimore
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Matrix Models, Gauge-Gravity Duality, and Simulations on the Lattice (Lecture 2) by Georg Bergner
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Symmetries in QFT and Their Relationship With Category Theory (Lecture 1) by Lakshya Bhardwaj
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Global chiral symmetry, extra dimensions, and topology (Lecture - 02) by David B Kaplan
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Gauge-string duality in lattice gauge theories (Lecture - 02) by Sourav Chatterjee
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On October 2, 1919, Edith Wilson found her husband, US President Woodrow Wilson, unconscious on the floor of his private bathroom. The nation spent the next 17 months not knowing Wilson’s condition or prognosis. Woodrow Wilson's stroke changed world policy, our understanding of the presi
From playlist History without War
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From playlist Summer Time