| Author | : Drew Armstrong |
| File Size | : 41,7 Mb |
| Publisher | : American Mathematical Soc. |
| Language | : English |
| Release Date | : 08 October 2009 |
| ISBN | : 9780821844908 |
| Pages | : 176 pages |
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups by Drew Armstrong Book PDF Summary
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.