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Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups
Drew Armstrong, University of Miami, Coral Gables, FL
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Memoirs of the American Mathematical Society
2009; 159 pp; softcover
Volume: 202
ISBN-10: 0-8218-4490-3
ISBN-13: 978-0-8218-4490-8
List Price: US$72
Individual Members: US$43.20
Institutional Members: US$57.60
Order Code: MEMO/202/949
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This memoir is a refinement of the author's PhD thesis -- written at Cornell University (2006). It is primarily a desription of new research but also includes a substantial amount of background material. At the heart of the memoir the author introduces and studies a poset \(NC^{(k)}(W)\) for each finite Coxeter group \(W\) and each positive integer \(k\). When \(k=1\), his definition coincides with the generalized noncrossing partitions introduced by Brady and Watt in \(K(\pi, 1)\)'s for Artin groups of finite type and Bessis in The dual braid monoid. When \(W\) is the symmetric group, the author obtains the poset of classical \(k\)-divisible noncrossing partitions, first studied by Edelman in Chain enumeration and non-crossing partitions.

Table of Contents

  • Introduction
  • Coxeter groups and noncrossing partitions
  • \(k\)-divisible noncrossing partitions
  • The classical types
  • Fuss-Catalan combinatorics
  • Bibliography
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