Generalized associahedra via brick polytopes

Vincent Pilaud (1) , Christian Stump (2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 Leibniz Universität Hannover=Leibniz University Hannover

We generalize the brick polytope of V. Pilaud and F. Santos to spherical subword complexes for finite Coxeter groups. This construction provides polytopal realizations for a certain class of subword complexes containing all cluster complexes of finite types. For the latter, the brick polytopes turn out to coincide with the known realizations of generalized associahedra, thus opening new perspectives on these constructions. This new approach yields in particular the vertex description and a relevant Minkowski sum decomposition of generalized associahedra.

Mots clés: Coxeter-Catalan combinatorics; subword complexes; cluster complexes; generalized associahedra; Coxeter- sortable elements; Cambrian lattices; Cambrian fans

Domaines: Combinatoire [math.CO]

Vincent Pilaud, Christian Stump. Generalized associahedra via brick polytopes. 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), Jul 2012, Nagoya, Japan. pp.73-84, ⟨10.46298/dmtcs.3021⟩. ⟨hal-00778013⟩