Realizations of the Associahedron and Cyclohedron

Hohlweg, Christophe et Lange, Carsten E.M.C. (2007). « Realizations of the Associahedron and Cyclohedron ». Discrete & Computational Geometry, 37(4), pp. 517-543.

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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 and B respectively. The coordinates are obtained by an algorithm which uses an oriented Coxeter graph of type An or Bn as 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 fan. This settles a conjecture of N. Reading for cambrian lattices of these types.

Type: Article de revue scientifique
Mots-clés ou Sujets: Combinatorics; Computational Mathematics and Numerical Analysis
Unité d'appartenance: Faculté des sciences > Département de mathématiques
Déposé par: Christophe Hohlweg
Date de dépôt: 15 févr. 2016 15:02
Dernière modification: 20 avr. 2016 19:32
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