Generalized noncrossing partitions and combinatorics of Coxeter groups
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This thesis serves two purposes: it is a comprehensive introduction to the Catalan combinatorics'' of finite Coxeter groups, suitable for nonexperts, and it also introduces and studies a new generalization of the poset of noncrossing partitions. This poset is part of a
Fuss-Catalan combinatorics'' of finite Coxeter groups, generalizing the Catalan combinatorics.
Our central contribution is the definition of a generalization
We study the structure noncrossing'' set partitions in which each block has size divisible by $k$. Hence, we refer to $NC^{(k)}(W)$ in general as the poset of
It turns out that our poset