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 an oriented Coxeter graph of type A_n or B_n as the only input data and which specializes to a procedure presented by J.-L. Loday for a certain orientation of A_n. 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.

Authors and Affiliations

1. The Fields Institute, 222 College Street, Toronto, Ontario, M5T 3J1, Canada

   Christophe Hohlweg

2. Fachbereich fur Mathematik und Informatik, Freie Universitat Berlin, Arnimallee 3, D-14195 Berlin, Germany

   Carsten E.M.C. Lange

Corresponding authors

Correspondence to Christophe Hohlweg or Carsten E.M.C. Lange.

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