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Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups
 
Drew Armstrong University of Miami, Coral Gables, FL
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups
eBook ISBN:  978-1-4704-0563-2
Product Code:  MEMO/202/949.E
List Price: $76.00
MAA Member Price: $68.40
AMS Member Price: $45.60
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups
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Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups
Drew Armstrong University of Miami, Coral Gables, FL
eBook ISBN:  978-1-4704-0563-2
Product Code:  MEMO/202/949.E
List Price: $76.00
MAA Member Price: $68.40
AMS Member Price: $45.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2022009; 159 pp
    MSC: Primary 05;

    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
     
     
    • Chapters
    • Acknowledgements
    • 1. Introduction
    • 2. Coxeter Groups and Noncrossing Partitions
    • 3. $k$-Divisible Noncrossing Partitions
    • 4. The Classical Types
    • 5. Fuss-Catalan Combinatorics
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2022009; 159 pp
MSC: Primary 05;

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.

  • Chapters
  • Acknowledgements
  • 1. Introduction
  • 2. Coxeter Groups and Noncrossing Partitions
  • 3. $k$-Divisible Noncrossing Partitions
  • 4. The Classical Types
  • 5. Fuss-Catalan Combinatorics
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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