Generalized noncrossing partitions and combinatorics of coxeter groups
著者
書誌事項
Generalized noncrossing partitions and combinatorics of coxeter groups
（Memoirs of the American Mathematical Society, no. 949）
American Mathematical Society, 2009
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注記
"Volume 202, number 949 (third of 5 numbers)."
Includes bibliographical references (p. 155-159)
内容説明・目次
内容説明
This memoir is a refinement of the author's PhD thesis - written at Cornell University (2006). It is primarily a description 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.
目次
- Introduction
- Coxeter groups and noncrossing partitions
- $k$-divisible noncrossing partitions
- The classical types
- Fuss-Catalan combinatorics
- Bibliography.
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