Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups PDF Download

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Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups

Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups PDF Author: Drew Armstrong
Publisher: American Mathematical Soc.
ISBN: 0821844903
Category : Mathematics
Languages : en
Pages : 176

Book Description
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.
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