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non-crossing partition

Proceedings of the Edinburgh Mathematical Society (1)

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1 results

From permutahedron to associahedron
Part of
- Algebraic combinatorics
- Special aspects of infinite or finite groups
Thomas Brady, Colum Watt
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 2 / June 2010

Published online by Cambridge University Press:

30 April 2010, pp. 299-310
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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.