Myrto Kallipoliti ; Henri Mühle - 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) - https://doi.org/10.46298/dmtcs.2320
On the Topology of the Cambrian SemilatticesArticle

Authors: Myrto Kallipoliti ORCID1; Henri Mühle ORCID1

  • 1 Fakultät für Mathematik [Wien]

For an arbitrary Coxeter group $W$, David Speyer and Nathan Reading defined Cambrian semilattices $C_{\gamma}$ 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 $\gamma$-sortable elements, and show that this is an EL-labelling for every closed interval of $C_{\gamma}$. 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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Coxeter Groups,Weak Order,Cambrian Semilattices,EL-Shellability,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Klassische Kombinatorik und Anwendungen; Code: Z 130

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