Shellability of noncrossing partition lattices

By Christos A. Athanasiadis, Tom D. Brady, Colum Watt. 2005

59 citations recorded by the source corpus.

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type D n and those of exceptional type and rank at least three.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9bf6c8ffd8bfec61e0e11fc8b25772c971206a37

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Clusters, Coxeter-sortable elements and noncrossing partitions (2005, background): “In [1], it is shown that for c bipartite, the natural labeling of [1, c]T is an ELshelling with respect to the reflection order obtained from what we here call the”
Noncrossing partitions and the shard intersection order (2009, unknown): “10, due to [3, 4]) of the Möbius number of the noncrossing partition lattice NC(W).”
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (2006, methodology): “We have based this introduction on results of Carter [39], Brady and Watt [34, 35] and Bessis [17].”
Proof of the $$K(\pi , 1)$$ conjecture for affine Artin groups (2019, methodology): “ane Coxeter group W. Therefore the poset [1;w] is EL-shellable. This extends the analog result of Athanasiadis, Brady, and Watt for noncrossing partition lattices associated with nite Coxeter groups [ABW07]. 26 GIOVANNI PAOLINI AND MARIO SALVETTI The EL-labelings of nite noncrossing partition lattic”