Realizations of the Associahedron and Cyclohedron
We describe many different realizations with integer coordinates for the associahedron (i.e. the Stasheff polytope) and for the cyclohedron (i.e. the Bott-Taubes polytope) and compare them with the permutahedron of type A and B, respectively. The coordinates are obtained by an algorithm which uses a...
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| Veröffentlicht in: | Discrete & computational geometry 2007-05, Vol.37 (4), p.517-543 |
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| creator | Hohlweg, Christophe Lange, Carsten E.M.C. |
| description | We describe many different realizations with integer coordinates for the associahedron (i.e. the Stasheff polytope) and for the cyclohedron (i.e. the Bott-Taubes polytope) and compare them with the permutahedron of type A and B, respectively. The coordinates are obtained by an algorithm which uses an oriented Coxeter graph of type An or Bn as the only input data and which specializes to a procedure presented by J.-L. Loday for a certain orientation of An. The described realizations have cambrian fans of type A and B as normal fans. This settles a conjecture of N. Reading for cambrian lattices of these types. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1007/s00454-007-1319-6 |
| format | Article |
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| subjects | Algorithms Geometry Mathematics |
| title | Realizations of the Associahedron and Cyclohedron |
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