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The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
Christian Stump, Ruhr-Universitat Bochum, Germany.Hugh Thomas, Universite du Quebec a Montreal, Quebec, Canada.Nathan Williams, University of Texas at Dallas, Texas.
1. Introduction2. Background on Coxeter and Artin groups3. Subword complexes4. Noncrossing partitions5. Cluster complexes6. Sortable elements7. Positive $m$-eralized structures8. Conjectures on rational structures9. $m$-eralized structures in representation theory