Results 1 to 10 of about 39 (35)
EL-Shellability of Generalized Noncrossing Partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 In this article we prove that the poset of m-divisible noncrossing partitions is EL-shellable for every well-generated complex reflection group. This was an open problem for type G(d,d,n) and for the exceptional types, for which a proof is given case-by ...
Henri Mühle
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h-vectors of generalized associahedra and noncrossing partitions [PDF]
International Mathematics Research Notices, 2006 A case-free proof is given that the entries of the $h$-vector of the cluster complex $Δ(Φ)$, associated by S. Fomin and A. Zelevinsky to a finite root system $Φ$, count elements of the lattice $\nc$ of noncrossing partitions of corresponding type by rank. Similar interpretations for the $h$-vector of the positive part of $Δ(Φ)$ are provided.
Christos Athanasiadis +2 more
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$m$-noncrossing partitions and $m$-clusters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $W$ be a finite crystallographic reflection group, with root system $\Phi$. Associated to $W$ there is a positive integer, the generalized Catalan number, which counts the clusters in the associated cluster algebra, the noncrossing partitions for $W$,
Aslak Bakke Buan +2 more
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Bijections between noncrossing and nonnesting partitions for classical reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We present $\textit{type preserving}$ bijections between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis and Reiner. The bijections for the abstract Coxeter types $B$, $C$ and $D$ are new in
Alex Fink, Benjamin Iriarte Giraldo
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Submaximal factorizations of a Coxeter element in complex reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 When $W$ is a finite reflection group, the noncrossing partition lattice $NC(W)$ of type $W$ is a very rich combinatorial object, extending the notion of noncrossing partitions of an $n$-gon.
Vivien Ripoll
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Euler Characteristic of the Truncated Order Complex of Generalized Noncrossing Partitions [PDF]
The Electronic Journal of Combinatorics, 2009 The purpose of this paper is to complete the study, begun in the first author's PhD thesis, of the topology of the poset of generalized noncrossing partitions associated to real reflection groups. In particular, we calculate the Euler characteristic of this poset with the maximal and minimal elements deleted.
Krattenthaler, Christian +1 more
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Faces of Generalized Cluster Complexes and Noncrossing Partitions [PDF]
SIAM Journal on Discrete Mathematics, 2008 Let $Φ$ be an finite root system with corresponding reflection group $W$ and let $m$ be a nonnegative integer. We consider the generalized cluster complex $Δ^m(Φ)$ defined by S. Fomin and N. Reading and the poset $NC_{(m)}(W)$ of $m$-divisible noncrossing partitions defined by D. Armstrong.
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Generalized noncrossing partitions and combinatorics of Coxeter groups [PDF]
Memoirs of the American Mathematical Society, 2009 This memoir constitutes the author's PhD thesis at Cornell University. It serves both as an expository work and as a description of new research. At the heart of the memoir, we introduce and study a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and for each positive integer $k$.
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Möbius numbers of some modified generalized noncrossing partitions
Toyama mathematical journal, 2009 In this paper we will give a Möbius number of $NC^{k}(W) \setminus \bf{mins} \cup \{\hat{0} \}$ for a Coxeter group $W$ which contains an affirmative answer for the conjecture 3.7.9 in Armstrong's paper [ Generalized noncrossing partitions and combinatorics of Coxeter groups. arXiv:math/0611106].
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On maximal dihedral reflection subgroups and generalized noncrossing partitions
Proceedings of the American Mathematical SocietyIn this note, we give a new proof of a result of Matthew Dyer stating that in an arbitrary Coxeter group W W , every pair
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