Realizations of the associahedron and cyclohedron

Research paper by Christophe Hohlweg, Carsten Lange

Indexed on: 14 Sep '06Published on: 14 Sep '06Published in: Mathematics - Combinatorics


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 to the permutahedron of type A_n and B_n respectively. The coordinates are obtained by an algorithm which uses an oriented Coxeter graph of type A_n or B_n respectively as only input and which specialises 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 fans of these types.