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Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups

Drew Armstrong University of Miami, Coral Gables, FL
Available Formats:
Electronic 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 Click above image for expanded view Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups Drew Armstrong University of Miami, Coral Gables, FL Available Formats:  Electronic 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.

• 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 reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
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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 reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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