From Permutahedron to Associahedron

Details From Permutahedron to Associahedron From Permutahedron to Associahedron

2008-04-15

arxiv.org/abs/0804.2331v1

Mathematics

Combinatorics

14 pages

Scientific paper

For each finite real reflection group $W$, we identify a copy of the type-$W$ simplicial generalised associahedron inside the corresponding simplicial permutahedron. This defines a bijection between the facets of the generalised associahedron and the elements of the type $W$ non-crossing partition lattice which 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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