From permutahedron to associahedron

Thomas Brady, Colum Watt

    Research output: Contribution to journalArticlepeer-review

    Abstract

    For each finite real reflection group W, we identify a copy of the type-W simplicial generalized associahedron inside the corresponding simplicial permutahedron. This defines a bijection between the facets of the generalized associahedron and the elements of the type-W non-crossing partition lattice that is more tractable than previous such bijections. We show that the simplicial fan determined by this associahedron coincides with the Cambrian fan for W.

    Original languageEnglish
    Pages (from-to)299-310
    Number of pages12
    JournalProceedings of the Edinburgh Mathematical Society
    Volume53
    Issue number2
    DOIs
    Publication statusPublished - Jun 2010

    Keywords

    • associahedron
    • non-crossing partition
    • permutahedron
    • reflection

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