Myrto Kallipoliti ; Henri Mühle
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On the Topology of the Cambrian Semilattices
dmtcs:2320 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2013,
DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
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https://doi.org/10.46298/dmtcs.2320
On the Topology of the Cambrian SemilatticesConference paper
Authors: Myrto Kallipoliti 1; Henri Mühle 1
0000-0003-2188-6552##0000-0003-1888-7247
Myrto Kallipoliti;Henri Mühle
1 Fakultät für Mathematik [Wien]
For an arbitrary Coxeter group W, David Speyer and Nathan Reading defined Cambrian semilattices Cγ as certain sub-semilattices of the weak order on W. In this article, we define an edge-labelling using the realization of Cambrian semilattices in terms of γ-sortable elements, and show that this is an EL-labelling for every closed interval of Cγ. In addition, we use our labelling to show that every finite open interval in a Cambrian semilattice is either contractible or spherical, and we characterize the spherical intervals, generalizing a result by Nathan Reading.