Results 1 to 10 of about 1,190 (56)

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.
Thomas Brady, Jon Mccammond, Christos A Athanasiadis   +2 more
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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.
Drew Armstrong, Christian Krattenthaler
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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 $k$.
Drew Armstrong
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Möbius numbers of some modified generalized noncrossing partitions [PDF]

, 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].
Masaya Tomie
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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.
Eleni Tzanaki
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From m-clusters to m-noncrossing partitions via exceptional sequences [PDF]

Mathematische Zeitschrift, 2011
Let W be a finite crystallographic reflection group. The generalized Catalan number of W coincides both with the number of clusters in the cluster algebra associated to W, and with the number of noncrossing partitions for W.
Aslak Bakke Buan, Idun Reiten, Hugh Thomas   +2 more
exaly   +5 more sources

Möbius numbers of some modified generalized noncrossing partitions [PDF]

Möbius numbers of some modified generalized noncrossing partitions
In this paper we will compute the Mobius number of {NC⁽ᵏ⁾(W)╲mins} ∪ {0^} for a Coxeter group W which contains an affirmative answer to conjecture 3.7.9 in [1] Article Toyama mathematical journal, vol.37, 2015, Page 145 ...
Masaya Tomie
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On maximal dihedral reflection subgroups and generalized noncrossing partitions

Proceedings of the American Mathematical Society
In this note, we give a new proof of a result of Matthew Dyer stating that in an arbitrary Coxeter group W W , every pair
Thomas Gobet
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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, Idun Reiten, Hugh Thomas   +2 more
doaj   +1 more source