Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (Memoirs of the American Mathematical Society)
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (Memoirs of the American Mathematical Society) by Drew Armstrong
English | 2009 | ISBN: 0821844903 | 159 Pages | PDF | 1.29 MB
English | 2009 | ISBN: 0821844903 | 159 Pages | PDF | 1.29 MB
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.