From permutahedron to associahedron

Thomas Brady; Colum Watt

doi:10.1017/S0013091508000448

From permutahedron to associahedron

Thomas Brady, Colum Watt

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	299-310
Number of pages	12
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	53
Issue number	2
DOIs	https://doi.org/10.1017/S0013091508000448
Publication status	Published - Jun 2010

Keywords

associahedron
non-crossing partition
permutahedron
reflection

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10.1017/S0013091508000448

https://arrow.tudublin.ie/scschmatart/148Licence: CC BY-NC-SA

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title = "From permutahedron to associahedron",

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.",

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AU - Watt, Colum

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AB - 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.

KW - associahedron

KW - non-crossing partition

KW - permutahedron

KW - reflection

UR - https://www.scopus.com/pages/publications/77954467048

U2 - 10.1017/S0013091508000448

DO - 10.1017/S0013091508000448

M3 - Article

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VL - 53

SP - 299

EP - 310

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

IS - 2

ER -

From permutahedron to associahedron

Abstract

Keywords

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