The greedy flip tree of a subword complex

Vincent Pilaud (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

We describe a canonical spanning tree of the ridge graph of a subword complex on a finite Coxeter group. It is based on properties of greedy facets in subword complexes, defined and studied in this paper. Searching this tree yields an enumeration scheme for the facets of the subword complex. Two specific families of subword complexes provide relevant illustrations for this algorithm: on the one hand, this work extends the greedy flip algorithm for pointed pseudotriangulations of points or convex bodies in the plane; on the other hand, it is closely related to Coxeter sorting and Coxeter sortable elements in finite Coxeter groups, which are relevant to generate cluster complexes.

Domaines: Combinatoire [math.CO]

Vincent Pilaud. The greedy flip tree of a subword complex. Génération Aléatoire de Structures Combinatoires, Jun 2012, Bordeaux, France. ⟨hal-00713838⟩