Realizations of the Associahedron and Cyclohedron

Authors:
Christophe Hohlweg;Carsten E.M.C. Lange
Affiliations:
The Fields Institute, 222 College Street, Toronto, Ontario, M5T 3J1, Canada;Fachbereich fur Mathematik und Informatik, Freie Universitat Berlin, Arnimallee 3, D-14195 Berlin, Germany
Venue:
Discrete & Computational Geometry
Year:
2007

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Abstract

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.