Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (Memoirs of the American Mathematical Society) - Softcover

Armstrong, Drew

Softcover

ISBN 10: 0821844903 ISBN 13: 9780821844908

Publisher: American Mathematical Society, 2009

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2009
• Language: English
• ISBN 10: 0821844903
• ISBN 13: 9780821844908
• Binding: Paperback
• Number of pages: 159