Sources

Here are the sources I'm using so far; where possible I will try to post links to the pdf files for some of the articles. For others, I'll post links to their Journals' websites. I won't be using all the materials from the sources below .... just what I need as when when I need it.

General Introduction to (Coxeter) Groups

• Combinatorics of Coxeter Groups, Anders Bjorner & Francesco Brenti (2000)
  
• Reflection Groups and Coxeter Groups, James E. Humphreys (1990)
• Introduction to Coxeter Groups, Robert B. Howlett

Infinite Groups, Automatic Groups, Regular Languages, Automata etc.

• GROUPS , GRAPHS & TREES : An Introduction to the Geometry of Infinite Groups, John Meier (2007)
• Word Processing in Groups, David B. A. Epstein, J. W. Cannon, D. F. Holt, S. V.F Levy, M.S. Paterson, W.P. Thurston (1992)
• The Use of Knuth-Bendix methods to solve the word problem in Automatic groups, Journal of Symbolic Computation D. B. A. Epstein, D. F. Holt, S. E. Rees (1991) (available on request)
  
• The Warwick Automatic Groups Software , D. F. Holt (1994)

I don't know what category the rest of my sources fall in. They do however play significant roles in giving me material for the thesis.

• Regular Polytopes, H.S.M. Coxeter (1973)
• Cells in Coxeter Groups , Paul E. Gunnels
  
• The Cayley Graphs of Coxeter and Artin Groups , Carl Droms and Herman Servatius (1993)
• A Transducer Approach to Coxeter Groups , Fokko du Cloux (1999)
• Computation in Coxeter Groups , Bill Casselman (2001ish)

If I was doing this in graduate school ... I would probably be using this book. I have it in my possession but I doubt I will actually get around to using it:

• The Geometry and Topology of Coxeter Groups , Michael Davis (2007)
  

Why did I decide to do this

Because I told enough people that I would so I kind of had no choice ....

Initially, the main goal of my thesis was to study the various ways in which Cayley Graphs of Coxeter Groups (cagcogs) can be built (and possibly rendered).

I have recently been able to distill this to the following question:
Constructing Cayley graphs of Coxeter groups is an inherently exponential process.
(Multiply each generator by every other generator for every step in the process ... so a group with n generators and k steps needs [Summation(n^i) for 0 < i < k] multiplications) We know that Coxeter groups grow polynomially, using that and other known facts about Coxeter groups, can we build the cayley graph in anything less than exponential time?

My biggest challenge in writing this thesis has been the fact that Coxeter group theory is so vast. A lot is known about them, which means there is so much for me to learn. I'm however picking up what to learn as I go along rather than wading though the
theory for its own sake. I ran the risk of possibly not recognizing solutions when they might be staring at me in the face.

I think the hardest part of this thesis is actually getting the actual teXing done. For that reason, I won't spend that much time here. I'll only be posting pdf updates on what I've teXed so far.

Finally the main reason I created this blog was because I want feedback, lots of it, on any aspects of the thesis. I am hoping to use that to mitigate my limited knowledge of this topic. I also want to thank everyone, especially my thesis adviser and readers and anyone else who would have helped contribute to my learning this material by the time I'm done.

Enough talk ... time to teX ....