Generalized noncrossing partitions and combinatorics of Coxeter groups
Drew Armstrong
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
Kategorije:
Godina:
2009
Izdavač:
Amer Mathematical Society
Jezik:
english
Strane:
176
ISBN 10:
0821844903
ISBN 13:
9780821844908
Serije:
Memoirs of the American Mathematical Society 0949
Fajl:
PDF, 1.29 MB
IPFS:
,
english, 2009