What is a...Cayley graph?

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Goal.
Explaining basic concepts of (a classical course in) algebra in an intuitive way.

This time.
What is a...Cayley graph? Or: Graphs and groups.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.

Thumbnail picture.
The Cayley graph of the symmetric group S4 using the generators (1,2) and (1,2,3,4)

Material used.

Mathematica.

More on spectra of Cayley graphs.

#algebra
#galoistheory
#mathematics
  1. VisualMath
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Комментарии
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Thanks man, you are truly a gifted educator and expositor

narutosaga
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Thanks for the great visual explanations! @15:43 Since the graphs change based on the generators used, does this effect "well-defined"-ness when studying groups through Cayley graphs? Because the group is the same, but the graphs are changing. Therefore, do you think we can only study the relation between the group and the generators, rather than the group itself?

RahulMadhavan
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Thank you for the great explanation! Both categories and Cayley graphs are directed graphs; I wonder if there's any connection? Could this allow you to view groups as categories in another way than as a one object category?

thevikifalcon