Cette thèse est consacrée à l’étude de la transition liquide/solide amorphe. Cette transition se retrouve dans des systèmes thermiques (par exemple dans les verres moléculaires) ou athermiques (avec entre autres les milieux granulaires), à l’équilibre thermodynamique ou hors équilibre. Nous

April 29, 2011Für UnsShe had never before seen a rabbit with either a waistcoat-pocket, or a watch to take out of it, and burning with curiosity, she ran across the field after it Lewis CarrollThe following document, written under the supervision of Dr. reviewed by:

I would like to thank Prof. Dr. Torsten Braun, head of the Computer Network and Distributed Systems group (RVS), for supervising this work and for his insightful advises. Prof. Dr. Torsten Braun encouraged and motivated me to publish my research results and he provided me the opportunity to present the work on various conferences, for which I thank him. I would also like to thank Prof. Dr. Roger Wattenhofer, responsible for the Koreferat of this work. Also, Prof. Dr. Oscar Nierstrasz who was willing to be the co-examinator of this work deserves many thanks. Many thanks go to my colleagues of the RVS group and of the IAM for our various interesting discussions about all kinds of topics and for making the institute a very pleasant and friendly place to work at. Special thanks go to David Steiner, Marc Steinemann, Matthias Scheidegger, Florian Baumgartner, Ruy De Oliveira, and Attila Weyland. There are many students who worked with me and helped a lot in developing and implementing. Among them I especially thankful to Thomas Bernoulli,

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mcmxciv This thesis deals with combinatorics in connection with Coxeter groups, finitely generated but not necessarily finite. The representation theory of groups as nonsingular matrices over a field is of immense theoretical importance, but also basic for computational group theory, where the group elements are data structures in a computer. Matrices are unnecessarily large structures, and part of this thesis is concerned with small and efficient representations of a large class of Coxeter groups (including most Coxeter groups that anyone ever payed any attention to.) The main contents of the thesis can be summarized as follows. • We prove that for all Coxeter graphs constructed from an n-path of unlabelled edges by adding a new labelled edge and a new vertex (sometimes two new edges and vertices), there is a permutational representation of the corresponding group. Group elements correspond to integer n-sequences and the nodes in the path generate all n! permutations. The extra node has a more complicated action, adding a certain quantity to some of the numbers.

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