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

(author)
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Paperback 159 Pages / Published: 30/11/2009
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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.

Publisher: American Mathematical Society
ISBN: 9780821844908
Number of pages: 159

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