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From permutahedron to associahedron

Part of: Algebraic combinatorics Special aspects of infinite or finite groups

Published online by Cambridge University Press:  30 April 2010

Thomas Brady  and
Colum Watt
Thomas Brady
Affiliation:
School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland (tom.brady@dcu.ie)
Colum Watt
Affiliation:
School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland (colum.watt@dit.ie)
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Abstract

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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.

Keywords

reflectionpermutahedronassociahedronnon-crossing partition

MSC classification

Secondary: 20F55: Reflection and Coxeter groups 05E15: Combinatorial aspects of groups and algebras
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 2 , June 2010 , pp. 299 - 310
Copyright
Copyright © Edinburgh Mathematical Society 2010